General Structures Flashcards
PROs and CONs of long span steel trusses.
PROs:
1 - large column free spaces
2 - prefabricated members reduce construction time and result in cost savings
3 - mechanical systems can be located in the open wedding
4 - high strength to weight ratio.
CONs:
1 - a lack of redundancy can increase the risk of failure
2 - large prefabricated members may post transportation difficulties
3 - member components will expand and contract with subject temperature changes
4 - deflection, the limited in comparison with the beam is usually due to a high standard death ratio or deformation or slippage of the member joins the flexion must be limited to avoid ponding
Gusset Plate Steel Truss Connection
Normally 3/8” or 1/2” thick it is used to allow a bolted or welded connection of truss members. Connectors are located on gage lines that intersect at theoretical panel points. A minimum of two bolts are required at each member. Center-to-Center spacing of holes and the spacing to the edges of plate must follow specified dimensions that are based on the connector diameter and the thickness of the plate.
At what location does failure usually occur in long span structures?
At the connections.
A lack of redundancy in the connections may result in progressive failure of the entire structure. It is advisable to incorporate stronger connections or more conservative designs at the calculated points of initial failure in addition to the code requirements. Shear is critical at the supports, so connections of the components being connected must have sufficient area.
Centroid
Also called the center of gravity.
In equations, this is the point at which the cross-section is considered to be concentrated. If a section has an axis of symmetry, this axis will pass through the center of gravity. Most structural calculations are based on cross-section properties that use axes passing through the centroid as the axis of reference.
Moment of Inertia (I)
Stiffness: the property of the cross-section of a member that enables it to resist deflection. It is a rating based on the cross-section of a material, which can be computed with the equation for deflection by substituting (I) for _/_ (deflection).
For example, /_ = PL3/48EI can be changed to I = PL3 / 48E/_
Where:
P = load
L = length
E = elasticity (29,000 Ksi for A36 steel)
For rectangular sections, Ix = Bd3/12 moment of Inertia is measured in in4.
Why does some degree of deflection occur in beams?
It occurs because a beam must develop internal resistance equal to the external force in order to achieve equilibrium. This allowable beam deflection is usually determined by code to prevent finishes from being damaged or cracked and is typically limited to 1/360 of span for live loads on roofs and floors, or 1/240 of span for dead load plus live load
Shear (V)
An action that occurs when two loads, parallel and opposite in sense, act on a body and cause the particles within the body to slide past one another. A shear diagram describes what the beam is doing in terms of sheer stress, its maximum shear capacity, and where the shear value of zero occurs (the point of maximum moment). The amount of maximum shear (from the shear diagram) along with the allowable shear stress of the material, determine the required area of the member necessary to resist shear.
Crystal Palace
Designed by Joseph Paxton for the Great Exhibition in London in 1851. It is one of the first buildings made of cast iron, glass panels and prefabricated components. This building is the precedent for most high-tech architecture which uses off-the-shelf, pre-manufactured components.
What criteria should an architect consider when choosing a structural system?
1 - Economy, materials and labor.
2 - Structural requirements, load resistance.
3 - Construction feasibility.
4 - Occupancy and building program.
5 - Relationships to other building systems such as HVAC.
6 - Construction schedule.
7 - Aesthetics and integration with building details.
8 - Cultural impact, material selection, etc.
Typically used for structural spanning units, and most effective where limited thickness is available are both characteristics of:
A - A Bond Beam
B - Pre-stressed Concrete
C - Lightweight Concrete
D - Post-Tensioned Concrete
B - Pre-Stressed Concrete
High-strength steel cables are placed in tension inside the concrete member either before or after curing. The internal compressive stress or reverse bending stress (seen as camber), components for anticipated loads as well as the weight of the member itself. When proper compressive stress is achieved, the major advantage is the reduction of tension cracking. It has longer spanning and heavier load-carrying capacity than ordinary reinforced concrete of the same thickness and depth.
A bond beam is a construction technique used to horizontally reinforce a course of a concrete masonry unit wall with steel rebar and concrete.
Lightweight Concrete can have superior thermal insulation and fire protective qualities, but it usually results in lower strength.
Post-tensioned concrete is a specific type of pre-stressing where reinforcing steel cable strands are placed in tension after the concrete has cured. A sleeve separates the strands from the concrete.
Which materials have the greatest long-term deflection?
Steel, Wood, Glass, Reinforced Concrete.
A - Steel and Wood
B - Steel and Reinforced Concrete
C - Wood and Glass
D - Wood and Reinforced Concrete
D - Wood and Reinforced Concrete
Wood will deflect 50% more than its initial deflection due in part to a decrease in moisture content.
Reinforced concrete continues to deflect for 2-5 years. Final deflection may be as much as 2.5 to 3 times greater than the initial deflection.
Deflection is controllable, to a degree, by proper detailing. Long-term deflection and shrinkage is known as creep.
Live Load
All loads other than dead loads that can occur in a structure, that is, all non-permanent, movable loads. Temporary, often dynamic loads (including rain, snow and ice) imposed by people, furniture, machines, equipment (elevators) and other non-structural elements.
Commonly referred to as the gravity loads on floor and roof surfaces. With respect to roofs it is considered a uniformly distributed load and with respect to floors it represents the probable effects due to occupancy.
Building codes provide minimum design requirements for different occupancies.
In a structural member, the result of the interaction between the concrete and the steel reinforcing bars is known as:
A - Anchorage
B - Bond Stress
C - Resistance
D - Embedment
B - Bond Stress
In the design of reinforced concrete structural members, strength is achieved by bond stress development. This stress occurs in the reinforcing bars when the member is subjected to a load. Reinforcing bars are required to resist the pull-out tension force. Strength is achieved through the bond between the steel and the concrete. The surface of the reinforcing bars are formed to have a pattern of deformations, which are governed by ASTM specifications. These ridges cause a mechanical interlocking of the concrete and steel.
Composite Beam
A reinforced concrete slab supported by a steel member that acts as a single structural unit to resist bending stresses. The concrete slab acts as the top flange and resist the compressive bending stress. The bond between the materials is made by welding steel studs to the top of the beam which creates a shear transfer between them.
Much stiffer than a non-composite beam, however, composite beams maybe shallow and deflection should be checked.
What building incorporated the concept of a suspension bridge?
The Federal Reserve Bank Building in Minneapolis
Designed by Gunnar Birkerts. Two sets of steel cables in the shape of a catenary curve support the vertical load of the building and are anchored to two concrete towers. In addition, a truss in compression is used between the towers to resist inward thrust.
Another building that incorporates suspension is the Hong-Kong Shanghai Bank by Sir Norman Foster. In this building, Foster ‘hangs’ the loads by trusses that transfer the load to four large trussed masts at the corners.
John A. Roebling is most notable for his design of the:
A - Brooklyn Bridge
B - Empire State Building
C - U.S. Capitol
D - Flatiron Building
A - Brooklyn Bridge
A suspension bridge spanning the East River from Manhattan to Brooklyn, begun in 1868. Assisted by his son Washington Augustus Roebling, he pioneered the idea of using steel wire instead of iron for suspension and cables.
The Empire State Building in New York City, 1930-32, is by Shreve, Lamb and Harmon.
The U.S. Capitol building in Washington D.C., 1793, is by Dr. William Thornton; though there have been significant modifications and additions by others.
The Flatiron Building is in lower Manhattan, New York, 1902, is by Daniel Burnham.
With regard to structural design, the weight of the structure including any permanent equipment is considered a:
A - Live Load
B - Dead Load
C - Working Load
D - Vertical Load
B - Dead Load
The gravity load is always applied vertically and is the sum of all permanent structural and nonstructural components of the building. It is generally considered an advantage in resisting overturning moment and sliding due to wind pressure.
However, it is a disadvantage during an earthquake because dead load or mass is directly proportional to the lateral seismic force. In the design of beams, the weight of the beam itself is considered a uniformly distributed dead load.
The structure of a building is designed to resist:
A - Stess
B - Strain
C - Deformation
D - Force
D - Force
These actions cause a push or pull on a body which resists by changing shape or deforming. Force includes magnitude, point of application, and line of action (the vector quantity). Force is measured in either kips or pounds (1000 lbs. = 1 kip).
Load is an applied external force.
Stress is an internal resistance per unit area to an external load.
Where does the maximum horizontal shear stress occur in steel and wood beams?
In steel the maximum horizontal shear stress (V) occurs at the neutral axis at the closest point to the supports.
In wood, shear is spread throughout the beam. The greatest amount of sheer is in the center of the beam at the supports.
Horizontal shear will always occur with vertical shear. In both wood and steel, vertical and horizontal shear are equal in magnitude and perpendicular to each other.
Define the following:
1 - Bearing Wall
2 - Non-bearing Wall
1 - A compression element used to support a load in addition to its own weight. It may be solid, comprised of a framework, or have openings for doors and windows provided they are sufficiently braced. Load-bearing walls are also used as shear walls, that is, to resist horizontal forces in their own plane, in addition to vertical forces.
2 - This element supports only its own weight with no other vertical loading, such as a simple partition. By code, it supports less than 200 lbs. per linear foot in concrete construction and less than 100 lbs. per linear foot in wood construction. In order to resist forces perpendicular to the plane, additional transverse bracing is necessary, for example, spreading at the base, stiffening with ribs, or external bracing.
A load is any effect that causes resistance in a structure, name the various types of loads that a building must resist.
1 - Dead Loads: Permanent Gravity Loads.
2 - Live Loads: Use and occupancy loads
3 - Combination: Dead load and live load plus snow, wind, or seismic loads.
4 - Vertical & Lateral Loads: Gravity and horizontal loads such as wind or seismic forces.
5 - Dynamic Loads: Often called impact loads. The result of elevators, cars, moving equipment, etc.
6 - Hydrostatic Pressure: Soil and water.
7 - Thermal Loads: Expansion and contraction due to changes in temperature.
Where does one obtain live load values for different buildings?
What are some typical values?
Live loads are specified in model codes and based on building Occupancy or Use. Dead loads are obtained from manufacturer’s literature or from construction manuals that give weights and densities of different materials, components , or assemblies.
Typical uniformly distributed live loads:
Residential, classrooms, hospital rooms - 40 psf
Offices, projection and control rooms - 50 psf
Fixed seating assembly areas, labs, reading rooms - 60 psf
Bowling alleys, marquees - 75 psf
Lobbies, moveable seating, balconies, corridors, gyms, ballrooms, fire-escapes - 100 psf
Wholesale stores, light manufacturing - 125 psf
Library stacks - 150 psf
When there is Occupancy or Use change in an existing building (especially in the rehabilitation of historic buildings) the live load capability of the building must be checked. This is done to ensure that the existing structure will satisfy the new live load requirements.
The allowable design stresses for visually graded lumber are based on what characteristics?
The species of wood, it’s grade, size, use, and it’s direction of loading.
The most common species of wood in construction are Southern Pine and Douglas Fir Larch. These species come in different grades such as (Select Structural, No.1, No.2, No.3, etc.)
The size of wood refers to the dimensions such as 2x4 or 2x12.
The use of the lumber depends on its classification (boards, dimension, timbers).
The direction of loading refers to the direction of the load with respect to the material. A wood member could be subjected to shear (Fv), and bending stresses (Fb) or tension (Ft) and compression (Fc) (parallel or perpendicular to the grain).
With regard to their structural characteristics, what is the relationship between the hinges and points of contraflexure?
1 - Both hinges and points of contraflexure are points of zero moment.
2 - A point of contraflexure may move as loading conditions change.
3 - A hinge is built into the structure and cannot move. It is located by the designer and must be detailed to act as a hinge.
The strength of concrete is determined by what factors?
1 - The Water-Cement Ratio: The most critical factor in obtaining the proper curing and maximum strength of the concrete. Too much water causes excessive shrinkage and can allow the ingredients in the mix to segregate. Too little water (although less water produces very strong concrete) will make the mix less workable and will prohibit the concrete from bonding with the aggregate. The amount and type of cement is also important.
2 - Admixture: Material other than water, cement or aggregate, added to the concrete to change its properties such as accelerators, retarders and air-entertaining agents.
A - _Fine Aggregate_: Coarse sand will produce grainy surfaces and can cause difficulty in finishing. Excessively fine sand will require additional water resulting in weakness and shrinkage. B - _Coarse Aggregate_: This represents the bulk of the mix. The properties of the aggregate; size, shape, material and quantity must all be considered for optimum strength, weight and fire resistance.
What factors would cause a decrease in the allowable bending (Fb) for a wood beam?
1 - Beam Shape: Most beams are rectangular in section, adjustments can be made for other shapes such as round.
2 - Beam Size: Beams larger than 12” nominal depth have reduced value of Fb
3 - Grade of Wood: Varies depending on quality. The better the Grade, the higher the Fb. A No.1 grade of a certain species is better than a No.3.
4 - Duration of Load: Dependent upon the amount of time the member is subjected to a load.
5 - Beam Stability: Adjustments are made for beams prone to compression buckling.
6 - Moisture Conditions: Kiln dried grade (15% MC) has higher Fb than air-dried grade (19% MC).
Note: Design loads for visually graded lumber are based on species of wood, size, use and direction of loading.
Shear stress is NOT the most critical factor in the design of a _________ beam.
A - Wood
B - Concrete
C - Steel
D - Heavy Timber
C - Steel
Although shear stress occurs in all beams, wood and concrete beams are most susceptible. Wood, in particular, is susceptible especially to horizontal shear. Beams that are heavily loaded and have a short span are often governed by shear. The main concern in the design of a steel beam is deflection and sometimes bending, when the compression flange is not adequately braced. Unless a large concentrated load is placed close to the support or it is a short span, steel is seldom governed by shear.
Describe the structural relationship between a cable suspension structure and an arch.
They are nearly structural opposites.
Although their loads are resisted by horizontal and vertical reactions, an arch is in compression and a cable structure is in tension. The arch has thrust acting outward and the cable has thrust acting inward. The arch tends to spread out at the base and the cable pulls in at its supports. The rise of the arch is like the sag of the cable which forms a catenary curve. Thrust decreases as the height of the arch increases and also decreases as the sag of the cable increases. A cable (flexible) will change in shape as the loads change whereas an arch (rigid) cannot.
Name FIVE factors that effect Bond Stress Development.
1 - Steel Strength: If the strength of the steel reinforcing is increased, the allowable stress is also increased which requires the need for greater bond stress or embedment lengths.
2 - Concrete Strength: If the specified compressive strength of the concrete is increased, the potential for bond strength development is also increased.
3 - Reinforcing Bar Size: An increase in rebar size will increase the ability of the bar to resist tension forces.
4 - Encasement: If the concrete mass around the reinforcing bar is limited, due to spatial requirements, the capability of the mass to develop bonding force may also be limited.
5 - Rebar Location: The concrete near the bottom of the pour cures more slowly, has a higher density and is of better quality due to the weight of the concrete above it. The capability of bond development is affected by this difference in quality.
Development Length
With regard to reinforced concrete design, it is the length of embedment of reinforcing bar necessary to develop the required design strength of the reinforcing at points of maximum stress.
One method of achieving the anchorage is to bend the end of the bar into a hook. When construction details limit the ability to extend the reinforcing bars sufficiently, a standard hook may be used to achieve adequate anchorage. The deformations on the surface of the rebar enhance bonding to the concrete and improve anchorage.
What are the PROs and CONs of precast concrete construction?
PROs:
1 - Faster Construction Time: No on-site tying of reinforcing, no assembly and removal of formwork, no curing time.
2 - Economy: Elimination of formwork construction allows for a significant reduction of on-site labor costs.
3 - Quality Control: Factory produced components are more consistent in quality, and uniformity of strength, density, color, finishes, etc.
4 - Standard Elements: Pre-designed and engineered components can reduce the time necessary for the design development phase.
CONs:
1 - Transportation: Often sizable, heavy and bulky, these members may pose significant difficulty in transportation to the site. Larger members will require a larger capacity crane.
2 - Cost: Manufacturing, transportation and handling costs may be comparable to the savings gained in the reduction of on-site construction time.
3 - Connections and Details: These members lack the continuity, stability and resistance to lateral forces found in cast-in-place concrete construction and may impede the integration of other building materials.
4 - Form: Sculptural possibilities are limited in comparison to those achieved in cast-in-place concrete.
Plywood ‘Type’, according to the Hardwood Plywood Manufacturer’s Association (HPMA) refers to what?
A - Grade
B - Durability
C - Core Construction
D - Wood Species
B - Durability
Durability is the capacity of the plies to withstand different exposure conditions and remain bonded together. This capacity is a function of the adhesive used in the construction of the panel.
Two main ‘types’
Type 1 - Exterior: Made with waterproof adhesive. Must withstand full weather exposure.
Type 2 - Interior: Made with water-resistant adhesive. Must resist occasional wetting.
Grade refers to the visual quality of the face veneer.
Core Construction refers to the material used for the inner plies.
Wood Species is a way of classifying plywood by category (construction or decorative), and hardwood or softwood.
What is a pneumatic structure and describe its characteristics?
An impervious fabric membrane supported by interior air pressure greater than the natural atmospheric pressure. Generally a tension structure that may occasionally be subjected to compression or bending. Commonly used as a roof enclosure for warehouses, athletic fields, etc. It can simply be inflated like a balloon using fans.
When the necessary tension in the membrane exceeds its strength, it must be reinforced. This is usually done by wrapping the membrane in a grid of steel cable. The resulting tension in the cables gives the building it’s form.
In addition, another type of pneumatic structure consists of a hollow ribbed element that gains rigidity through its own internal pressure, independent of the internal pressure of the space, and may be used as a wall, a roof or both. Inherently flexible, these structures are dependent on the pressure differential between interior and exterior air to support even their own weight. Because of their exceptionally light weight, consideration of wind forces is critical since it may cause the structure to flutter. Uneven wind pressure (windward/leeward) may cause non-uniform loads which are detrimental to the structure.
Unlike traditional compression foundations, pneumatic structures need tension foundation to tie them down.
Define Camber
A convex or upward curvature built into a beam, truss or slab intended to counteract deflection when subjected to an anticipated load. Especially when the dead load represents the majority of the load. Common in pre-stressed concrete, it is intended to result in a nearly level or flat member after all service loads are applied. In light frame wood construction, this curvature is not intentional, however, the member is installed with the curve up to limit deflection.
Truss Design Characteristics
Typically, for all truss members to be in pure axial compression and tension, loads are placed at the panel points (truss joints). Loads placed between panel points will cause bending moments in the loaded member and should be avoided. Members that are loaded in-between panel points will end up larger in area since they will be subjected to combined (axial & bending) stresses. Regarding open web steel joist (K, LH, DLH), these units are designed on the basis of a uniformly loaded top chord. Beams or girders must be placed under concentrated loads since open web steel joists are designed for uniform loads only.
What are the characteristics of beam deflection with regard to long-term loading?
Steel: No effect to consider
Timber: Immediate deflection is computed with the standard formulas similar to those found in AISC manual. A long term factor of up to 2 is then applied.
Concrete: A special computation for moment of inertia (I) is required. The modulus of elasticity (E) is an estimate but otherwise immediate deflection is computed normally as per AISC manual. Long-term factors are considered a percentage of the load always in place. Creep is the term associated with the long term deflection of concrete members.
What materials are allowed in the construction of a shear wall?
1 - Reinforced Concrete
2 - Reinforced Masonry
3 - Structural Steel
4 - Plywood or other sheet material on studs. Nailing patterns are an important factor in this construction.
This type of wall is designed to resist lateral forces, such as wind or earthquake loads, in its own plane. This wall can also be designed as a braced frame or a bent, which resists loads through the development of axial stresses.
In a reinforced concrete beam, how does design for positive moment differ from design for negative moment.
The computations look the same for each, however, the location of the reinforcing steel is different. Reinforcing steel is located at the tension face of the beam. For positive moment (all simply supported beams) the steel is located toward the bottom of the beam. For negative moment (overhangs and cantilevers) the steel is located toward the top of the beam.
What are the PROs and CONs of lift-slab construction?
In this structural system, two-way concrete slabs are site-cast on top of each other on the ground slab, and then raised into place using special hydraulic jacks. The slabs are then attached to the columns.
PROs
This method requires little supported formwork. This can result in a lower construction time and lower labor cost. In addition, this method offers ease of concrete placement.
CONs
Satisfactory slab-column connections can be difficult to achieve and are not moment-resisting (pinned). This can be a problem when the system is subjected to lateral loads. Building plan must be highly repetitive, otherwise this method is not economical.
With regard to a roof structure, ponding means that the roof:
A - Is designed to retain water for a downfeed system
B - Has drains that are installed incorrectly.
C - Is being sprayed with waterproof material.
D - Has deflected and water will not drain.
D - Has deflected and water will not drain.
This phenomenon is a result of excess deflection of the roof structure and causes water to collect. It usually occurs in a roof that is too flat (less than 1/4” per foot). Water is unable to reach the drains and continues to collect as deflection increases. In extreme situations, it will lead to accelerated roof failure, particularly in long-span roofs.
Note that water weighs 62.4 lbs. per cubic foot (PCF).
What are the THREE most common two-way concrete structural systems?
1 - Flat Plate: The simplest system. It is used for light loads and short spans, because it can’t accommodate large shear loads near the columns.
2 - Flat Slab: Similar to the flat plate, but has thicker drop panels near the columns to handle shear loads. Best used in rectilinear buildings when columns are in line and equally spaced.
3 - Waffle Slab: Used for heavier loads and longer spans up to 40’.
Why is it important to calculate shear (V) in beams?
To determine if there is enough cross-sectional area in a beam to prevent shear failure. This typically occurs at the supports where the value of shear is highest. A significant location on the shear diagram is that of zero shear, with it being has the greatest potential for failure in bending. The location on a beam where the shear value(s) equal zero coincides with the point(s) of maximum moment.
Calculate the design load for an Open-Web steel joist spaced 3’ on center and supporting a load of 175 psf over a span of 24’
3’ x 175psf = 525 pounds per linear foot.
Multiply the joist spacing by the uniform load being supported (lbs./s.f.) to determine the load per linear foot.
PROCEDURE: Go to the table with the joist span (24’) and the load per linear foot (525 lbs. per linear foot) and select the lightest member that will work from the steel joist load table.
Which of the following is the most important in column design?
A - Overturning
B - Shearing
C - Twisting
D - Buckling
D - Buckling
A column is a vertical structural compression member that transmits axial loads through its longitudinal axis. The chance of buckling is the main concern in column design. The chance of buckling increases as the unbraced length and the slenderness ratio (SR) increase. The degree of buckling is determined by the stiffness of the member. The larger the slenderness ratio, the greater the chance of buckling and the less compressive stress the column can withstand.
What critical factor limits the load-carrying capacity of a short wood column?
Bearing Capacity
Bearing Capacity limits the load-carrying capacity of a short wood column and is a greater concern than buckling. Bearing in compression parallel to the grain is dependent upon the mass of the material and its stress limit in compression. In a short column, the ratio of length-to-width is relatively small, which permits a larger allowable stress and reduces the possibility of column failure due to buckling.
In a simply supported steel beam, shear is resisted mostly by the:
A - Web
B - lbs./linear foot
C - End Condition
D - Flange
A - Web
In wide flange shapes and I-beams, although most of the material lies in the flanges, it is the area of the web that resists shear. The deeper and thicker the web of a steel beam is, the greater its shear capacity. The material in the flanges is ignored with regard to shear.
In contrast, the flanges are primarily responsible for any bending moment. The wider the flanges and the further apart they are, the greater the moment-carrying capacity of a steel beam (greater section modulus).
Define underpinning and describe when it would be used.
This is the process of rebuilding, stabilizing or strengthening the foundation of an existing building. Three possible solutions are to enlarge the existing foundation, insert a new, deeper foundation under the existing one or treat the soil directly to increase bearing capacity.
This may be necessary for several reasons. Typically it is due to the excavation necessary for the construction of an adjacent building with a deeper foundation.
A number of potential problems can occur at closely spaced footings set at different levels. Excavation for the new building my disturb the soil around the existing foundation and must be done in a way that will not cause the existing foundation to settle or fail. Any settlement of the lower footing may cause additional settlement of the upper footing. Additionally, if the upper footing is carrying a significanrt load, the pressure in the soil below it may cause additional lateral load on the lower footing.
How can maximum moment be determined from a shear diagram?
The moment of any section of a simply supported or continuous beam is equal to the sum of the areas under the Shear Diagram to the left of the section. The location of zero shear is the point of maximum moment. Remember, in shear diagrams, vertical increments represent force (lbs.) and horizontal increments represent span (feet).
What structural members are statically indeterminate?
Beams that rest on more than two supports (continuous beams) or beams that are fixed or partially fixed at one or more supports to resisit rotation, (fixed-end beams) and rigid frames for example.
The bending moment cannot be determined by using only the equations of static equilibrium, Additional information is required regarding the elasticity of the material and the size of the members (E and I).
Name the two types of structural bolts used to connect steel members.
1 - Unfinished A-307
They have the lowest load capacity due to their limited shear strength. Some movement occurs in the development of full resistance. Nuts are tightened enough to ensure a snug fit. Used for minor connections.
2 - High-Strength A-325 or A-490
Nuts are tightened sufficiently to create a tension force that causes a high degree of frictional reistance between the parts.
High-Strength designations are:
F: The limiting resistance is friction between the joined materials. N: FUnction in bearing and shear. Threads are not excluded (included) from shear planes. X: Similar to N, but threads are excluded from shear planes.
What is the difference between the Resultant of two or more forces and the Equilibrant of the same forces?
Resultant
The Resultant of two or more forces acting on a body is a single force that has the same cumulative effect on the body as all the forces it replaces.
The resultant is a vectorial summation of two or more forces. Since the Resultant is a vector force, it follows that it is defined by a Point of Application (P.O.A.), a Magnitude, a Line of Action (L.O.A.) and a sense (arrowhead).
Equilibrant
The equiplibrant has the same Point of Application as the Resultant. It also has the same (or parallel) LIne of Action, and Magnitude. However, the Equilibrant has a sense (arrowhead) opposite to that of the Resultant.
The Equilibrant brings the Resultant to equlibrium
Motion of:
1 - Translation
2 - Rotation
Although buildings are not supposed to move, their motion, however small, as a response to an applied force is a major consideration in structural design.
1 - Translation: This type of motion occurs as a simple linear displacement, where the path of a moving point is a straight line (either up/down; or left/right).
2 - Rotation: This type of motion occurs if the path of a moving point can be measured angularly as it revolves around a fixed reference point in a radial manner.
In wood construction, expansion and contraction due to changes in moisture content is inevitable. At what point does green lumber begin to change size.
A - Below a moisture content of 11%
B - Below the fiber saturation point.
C- At equilibrium
D - Above 50% relative humidity
B - Below the fiber saturation point.
Green lumber has not been seasoned and has a high moisture content. Water is present in the cavities between the cells and is called free water. Water is also present in the cell fibers and is called bound or absorbed water. As wood dries, the free water evaporates first. The wood fibers are still fully saturated and this is called the fiber saturation point (in most species it is about 30% moisture content). Only when bound water begins to evaporate will the wood shrink and increase in strength. As the wood dries, the moisture content decreases and the strength increases. It is usually unnecessary to season framing lumber below a moisture content of 11%-13%, because at this point the wood will continue to shrink or swell in order to maintain equilibrium with the moisture content of the air. Small dimensional changes in a single member are usually not a concern. However, the total chnage of several members such as in a wood floor may cause gaps or buckling.
Ultimate Strength Design (USD)
The most common method used to calculate the strength of a concrete member. It is calculated by using a factorred design load called the uiltimate load. Code establishes the required strength (U) to be not less than:
U = 1.4D + 1.7L
Where D = Dead load and L = LIve Load. The new loads include the safety factor to be used in sizing and reinforcing the concrete member.
This is a different design method than that currently used on wood or most steel member calculations. Wood and steel members may be designed using the Allowable Stress Design (ASD) method. The trend today is to use the Load-Resistant Factor Design (LRFD) for designing steel members and a similar method for wood members.
The Flexure Theory
Internal Moment = External Moment (moment Diagram)
Internal bending stress in the fibers of the beam resist external bending moment caused by the forces acting on the beam.
Internal resisting moment is greater with an increase in depth. The issue of depth is critical in both span and load determination. The cross-sectional shape, area and materal of the beam act together to resist internal moment. Deflection is the strain that results from bending and needs to be limited to prevent excessive sagging. The allowable deflection is specified by model codes as a fraction of the span (1/180, 1/240, 1/360, etc.)
Truss
A system of compression and tension members that act together like a beam and can span very long distances. Composed of straight members, their intersections usually form a number of triangulations. Chord froces increase toward the center of the span as web forces decrease toward the center of the span.
Name the TWO end conditions for supporting the legs of an arch and the characteristics of each.
1 - Fixed: Does not allow for rotation at the base. This condition can cause a high bending moment at the mid span.
2 - Hinged: More common than fixed, this flexible condition allows for rotation at its base. This rotation counters the stresses caused by live load, thermal expansion or uneven foundation settlement. Low bending moment at the supports, high bending moment at the apex.
Note: The addition of a third hinged connection at the apex will reduce the bednign moment at mid span and makes the structure statically determinate.
Vonsider a 25’ steel rod placed in tension. The rod is now 0.35” longer than its original length.
What is the rod’s Unit of Elongation?
A - 0.000350 feet per foot
B - 0.001166 inches per inch
C - 0.016 feet per inch
D - 0.036 inches per foot
B - 0.001166 inches per inch
- 35 inches is refered to as the rod’s total elongation. Since the original length of the rod was 25’ (300”), the Unit of Elongation, or elongation per unit of length is
- 35/300 = 0.001166 inches/inch.
When subjescted to shear stress, wood members are weakest in which direction
1 - Perpendicular to tge grain
2 - Parallel to the grain
2 - Parallel to the grain
The main concern for shear in a wood beam is the longitudinal or horizontal splitting parallel to the grain (horizontal shear). This typically occurs at the ends of a simply supported wood beam.
Resistance to shear perpendicular to the grain (vertical shear) is relatively high in a wood beam.
Define Open-Web Steel Joists
Shop-fabricated trusses of various standard sizes and details, usually used to support roof and floor decks. Top and bottom chords are made of cold-formed steel or double angles. Web members consist of steel rods or formed steel angles sandwiched between the teh angles of the top and bottom chords. These members are light-weight and can span long distances. Since long span members are deep and slender they are susceptible to buckling, especially during construction. They depend on secondary framing members called bridging (cross-bracing) for full stability. Open-web steel joists are categorized as follows:
K - Standard
LH - Long Span
DLH - Deep Long Span
Details and load capacities are standardized by the Steel Joist Institute.
Which of the following is NOT true of a girder?
A - It spanse between columns or bearing walls.
B - It supports the axial load of a beam.
C - It transfers a load from a beam to a column.
D - It supports concentrated loads
B - It supports the axial load of a beam.
A girder is a large primary horizontal supporting member of steel, reinforced concrete or timber. While it does support the load of a beam, these are transverse (normal or perpendicular) loads, not axial loads. Columns or bearing walls are common supports for girders. A girder supports a beam, beams support joists, decks or slabs.
A Beam is a horizontal structural member that carries transverse loads such as those from a joist, rafter, or purlin. It spans between girders.
A Joist is one of a series of relatively light-weight prallel members that span between larger beams, girders or bearing walls. They are horizontal members used to support floor and ceiling loads. For wood members, typical spacing is 12”, 16” or 24” intervals, on center.
A Rafter is similar to a joist, however, it is installed at an incline and is used to support roof loads, whereas joists support floor or ceiling loads.
A Purlin is a horizontal member that spans across the slope of a pitched roof, parallel to the ridge beam and the header. Purlins are used to transfer roof loads from the decking to the rafters.
List some of the objectives of any building code.
The primary objective of any building code is to protect the life and safety of a buildng’s occupants. Other objectives include:
1 - To protect against structural failure in the event of a fire or earthquake
2 - To ensure that building components are assembled correctly.
3 - To ensure that the building materials are appropriate to a building’s function.
Accessibility, structural, mechanical, electrical, plumbing, and other codes have more specific requirements in addition to health, safety and welfare.
Some Structural concerns expressed in any building code include:
1 - Load determination
2 - Allowable stresses in structural members
3 - Formulas for designing members of various materials.
4 - Construction requirements.
With regard to concrete and timber, the result of creep is:
A - The sound generated by movement in the structure.
B - A lenghtening of the member that develops under a constant load.
C - A long-term shortening under a sustained compression load.
D - A loss of volume after the material is in place.
C - A long-term shortening under a sustained compression load.
This is the deformation of a member subjected to a high level of compression stress (load) over a long period of time. This deformation, or shortening, lessens over time and the amount of movement varies enormously depending upon the material and the load. It will cause columns to shorten, and an increase in beam deflection. Note that a portion of a beam’s cross-section is always in compression.
Name FIVE types of spread footings.
This is a type of foundation that distributes the building load over a large area of soil to ensure that the bearing capacity (Fp) of the soil is not exceeded.
1 - Wall Footing: placed under a continuous foundation wall and used to support a bearing wall.
2 - Isolated Pad Footing: supports a single column.
3 - Combined Footing: supports to or more columns
4 - Cantilever Footing: distributes the column load to each footing to equalize soil pressure
5 - Mat Footing: one large footing used for low soil bearing capacity or heavy loads.
Regarding foundations, describe TWO options for dealing with soil that is compressive or has low bearing capacity.
Shallow Foundation
Mat: A type of spread footing, acts like one large footing that distributes the load under the entire building.
Raft: Where the foundation is similar to a amt but the excavated soil is roughly the same weight as the building causing the building to essentially float.
Both are two-way slabs and can be stiffened by shear walls above the foundation.
Deep Foundation
Used in conjunction with a amt foundation are piles, where long stilts are driven into unstable soil and transmit the building load theough skin friction (perimeter surface area) or to a more stable layer of soil, that provides end bearing for the piles. Piers, or caissons, where a hole is excavated and filled with concrete are also used to support mat and raft foundations. The lower end may be belled to achieve the necessary bearing area.
What is the coefficient of thermal expansion?
This is the measure of the linear expansion of a material as it is heated (a). It has a unit of inches per degree Fahrenheit.
Values for typical materials are:
Lead: a = 0.0000159
Aluminum: a = 0.0000128
Copper: a = 0.0000093
A-36 Steel: a = 0.0000065
Concrete: a = 0.0000055
Timber (Fir): a = 0.00032 (perpendicular to the grain)
a = 0.0000021 (parallel to grain)
The similarity in the coefficients of concrete and steel make them complimentary materials. This is why steel reinforced concrete members or building components are exceptionally functional
With regard to structural failure, what is the main distinguishing factor in long span design?
A - The considerable amount of deflection
B - A weak column-beam connection
C - A lack of redundancy
D - The impact of lateral loads.
C - A lack of redundancy
Although failure of these members usually occurs in the connections it is most likely due to a lack of redundancy. Since there are realtively few members working together, a failure in one member may result in a progressive failure of the remaining structure. In these structures, deflection, as well as lateral loads are expected and included in the design of the members.
The reliability of each of the members is crucial, therefore, it may be adviseable to design additional connections at the calculated points of failure, above and beyond the minimum required by building codes.
Define the following:
1 - Subsidence
2 - Liquification
Subsidence
A widespread sinking of the ground surface or settlement of the soil mass. Some causes may include highly compressive organic material or loose fill, seismic events or the addition or removal of oil, gas or water which creates compressive void spaces.
Liquification
A sudden loss of shear resistance in the soil. It is the transformation of otherwise stable granular soil from a solid material to a material with liquid characteristics, such as sand. It can be the result of earthquakes or other vibrations in the earth’s surface.
What are the structural properties of ASTM A36 steel?
The most common type of steelfor structural applications. The designation ASTM means that the steel has been manufactured according to the requireemnts set by the American Society for Testing and Materials, and A36 is the specification number.
Yield Point: Fy = 36 ksi (specified minimum)
Specified Ultimate Tensile Stress: 58 ksi.
According to AISC:
Maximum allowable Stress: Fv in shear = 14.5 ksi (Margin of safety is between 14.5 and 36 ksi)
Maximum allowable Stress: Fb for bending = 24 ksi and depends on the adequacy of the lateral support of the compression flange.
Modulus of Elasticity: (E) = 29,000 ksi
Note: E refers to stiffness, not strength.
Moment (M)
The tendency of a force to create a rotation about a point. It is equal to the magnitude of the force multiplied by the perpendicular distance from the line of action (moment arm) to the point (center of mass).
For a simple beam with a distributed load: M = (WL)/8 or M = (wl2)/8
For a simple beam with a single concentrated load in teh center of the beam: M = (PL)/4
Maximum Moment occurs where the shear diagram crosses zero. moments are expressed in foot-pounds, inch-pounds, kip-feet, or kip-inches.
The amount of maximum moment (from the loading diagram) along with the allowable bending stress of the material, determine the required Section Modulus of the member necessary to resist bending moments.
Wood beam behavior begins to change at what beam depth?
Greater than 12” in depth.
Larger wood members often have undetected, internal flaws that reduce their load carrying capacity. As a result, the allowable stress in bending (Fb) must be decreased for larger members and is multiplied by a size factor (Cf) which accounts for beam depth.
Fb x Cf
Where: Cf = (12/d)1/9 and d = beam depth in inches
Cf is a fraction which is often close to 1 and is thus a slight reduction of Fb.
A simply supported wood beam deflects 1” under a certain uniform load and span. If the allowanble deflection is not to exceed 3/4”, what can be done to reduce the deflection?
Examine the terms in the deflection equation for a uniform load
_/_ = (5wl4)/(384I) = (5WL3)/(384EI)
1 - Decreasing the uniform load coefficient (w) by 25% will decrease _/_ from 1” to .75”
2 - Decreasing the span (L) will significantly decrease _/_
3 - Increasing the Modulus of Elasticity (E) will decrease _/_
4 - Increasing the moment of Inertia (I) will decrease _/_
A W12x106 steel section is to be used as a column and will carry an axial load of 600 kips. If the column is 20’-0” prior to loading, how much will it shorten?
Assume that AISC lists Area for W12x106 as 31.2 in2
A - 0.01326”
B - 0.1591”
C - 0.00796”
D - 0.001519”
B - 0.1591”
Since the change in Length = _/_L = (PL) / (AE)
P = 600 kips
A = 31.2 in2
E = 29,000 ksi
L = 20’ or 240”
Then: _/_L = (600 x 20 x 12) / (31.2 x 29,000) = 0.1591”
Define Concrete Design Strength (fc’)
Concrete Design Strength (fc’) is the maximum compressive strength of cured concrete.
Commonly designed to be 3,000 psi for general use. Strengths of 2,000 psi may be appropriate for some applications whereas 9,000 psi may be required for ground floor columns in tall buildings. Higher strengths (5-7,000 psi) are also required for pre-stressed and tilt-up concrete since they will be picked up by a crane and transported.
Slump tests can be performed during placement to determine the consistency of the mix, too wet or too dry, usually a result of the water/cement ratio.
However, strength tests called cylinder tests (cylindrical mold test), are performed on cured samples cast at the time of the pour. The cylinders, usually 6” in diameter by 12” high, are subjected to compression tests after a period of 7 days and again after the cured concrete has reached its Maximum Compressive Strength, in 28 days. Core Cylinder tests are performed by drilling a cylinder from cured concrete and subjecting the sample to compression to determine if it meets or exceeds the specified fc’.
Which properties of a cross-section are used in the design of the structural beams and columns?
1 - The geometric properties of the Area are analyzed and are independent of the material. The area of the section (and its material) determines its ability to resist shear.
2 - Every section has a Section Modulus (Sx). The section mudulus (in3) of the section (and its material) determines its ability to resist bending moments.
3 - Every section has a Moment of Intertia (Ix). The moment of inertia (in4) of the section (and its material) determines its ability to resist deflection. Both section modulus and moment of inertia have reference to a neutral axis passing through the centroid of the section. When the section is used along its strong axis Ix and Sx are used, and when used on its weak axis Iy and Sy are used.
4 - Every section has a Radius of Gyration (r). The radius of gyration (inches) is used mostly to determine the slenderness of a steel column.
5 - Every section has a Centroid, which is defined by the intersection of all neutral axes for the section (x-x, y-y, z-z).
A steel beam is subjected to a temperature change from 25ºF to 85ºF. Its original length at 25ºF was 65’-0”.
How much longer will the beam elongate?
A - 3.042”
B - 0.0255”
C - 0.3042”
D - 0.2574”
C - 0.3042”
The change in length (/_l) is equal to the change in temperature (/_T) multiplied by the coefficient of thermal expansion (a). Since the coefficient of thermal expansion of steel is 65’ x 10-7 in/in per degree Fahrenheit then:
_/_l = _/_T x : x a
_/_l = 60 x (65 x 12) x 0.0000065
_/_l = 0.3042”
Describe the procedure for sizing a timber beam.
Maximum moment and maximum shear must be known or calculated. Grade and species of timber will determine the allowable Bending Stress (Fb) and the allowable Shear Stress (Fv).
1 - Knowing the maximum moment about the x-axis and the allowable Bending Stress (Fb), compute:
Section Moduls Sx = (MMAX)/Fb. This will satisfy bending moment requirements.
2 - Section Modulus for rectangular sections: Sx = (bd2)/6
3 - Knowing the maximum shear (VMAX) and allowable Shear Stress (Fv) compute:
Area = (3VMAX)/(2Fv).
4 - Area for rectangular section A = b x d
5 - Select a member that has a larger area than found in 4, above and a larger section modulus than found in 2, above.
Note: Adjustments are to be expected since timber is supplied in standard sizes.
Identify the following beam-column connections
Identify the following Beam-Column connection methods
Identify these beam conditions
A - Simple Beam: Ressts on a support at each end. The beam ends are free to rotate.
B - Cantilevered Beam: Projects from its support and is fixed (restrained) at that support.
C - Overhanging Beam: End porjects past the support.
D - Continuous Beam: Supported by more than two supports.
E - Restrained Beam: Has one or both ends fixed and restrained against rotation.
In order tp design a beam, what criteria must be known?
1 - The span and support condition of the structure being designed and the uses proposed.
2 - The loads that will be applied (uniform, concentrated, variable).
3 - The weight of the beam itself. This must be estimated and adjustments must be made if estimate is shown to eb wrong. This is most important in concrete beams but should be checked in other materials. The span, loads, beam weight and support conditions will determines the resulting maximum shear and bending moment to which the beam will be subjected.
4 - The material to be used will determine the allowable stresses Fb and Fv and the Modulus of Elasticity (E). For steel beams the grade of steel must be known. For timber beams, the species (pine, fir, etc.) must be known, in addition to the grade (No.1 , No. 2, etc.). For reinforced concrete members, the strength of the concrete (fc’) and strength of the rebar (fy) must be known.
5 - The degree of lateral support for the compression side of teh beam (critical for steel beams).
In structural concrete members, reinforcing should be placed:
A - Near the top
B - Near the bottom
C - Near the tension face
D - Near the compression face
C - Near the tension face
This is the face that elongates under a load. In this case, the load of teh retained earth.
Compute the tributary area for column B-2 and the load transferred to it if:
Live Load = 100 psf
Dead Load = 80 psf
Tributary Area for column B-2 = 30’ x 25’ = 750 ft2
The load on the column = A x (load/ft2) = 750 x (100 + 80) = 135,000 lbs. or 135 kips
What is the condition at point A?
Point A represents the point of Maximum Bending Moment and Zero Shear, which occurs directly under the concentrated load.
Note that the right reaction is larger than the left since the concentrated load is applied to the right of midspan. The shear diagram under thge uniform load is sloping straight line and the moment diagram is a parabola. There is a sudden drop in shear under the concentrated load in the shear diagram.
What is the formula for Resistance of Bearing-Type Shear Connections?
R = Fv x A
Where:
R = Resistance to shear failure
Fv = Allowable shear stress
A = Area of bolt cross section
In a simple connection between two steal bars, the force (in this case tension) is transferred from one area to the other through the connector (bolt). Assume the bolt is loosely tightened and acts as a pin connection. While each plate is subjected to tension, the bolt itself is subjected to single shear. The amount of tension that each plate can handle depends on its srength (Fy) and dimensions (width and thickness). The amount of shear that the bolt can handle depends on its strength (A-325 or A-490), diameter and whether the threads are included in the plane of shear (type N) or excluded (Type X).
Identify the foundation system below.
Wall Foundation
A oad distributing, or spanning element, used in foundation systems. Often used to span unacceptable soil, it combines the functions of a foundation wall and a wall footing into a single structural element. May be self supporting or bear on piles.
Identify lines A and B
A - Hoops
B - Meridians
The meridian lines in a dome act as individual arches transferring loads through compression to the ground. This compression is countered by the hoops that are in compression in the upper portion and in tension toward the ground. One of the most efficient structural systems if it is not too flat (high rise-to-span ratio).
Calcualte the allowable axial load for a 10” x 12” wood column (Douglas Fir, Structural Select) with an unbraced length of 20’
82.156K (or 82,156 lbs)
Refer to steps 1-4 of this chart for help in calculating the allowable axial load.
Name the following steel column end conditions.
Note that the dashed line represnts the buckled shape of the column.
A - Rotation Fixed, Translation Fixed (strongest type). K = 0.5
B - Rotation Free (pinned), Translation fixed. K = 1.0
C - Rotation Fixed, Translation Free. K = 1.0
D = Rotation Free (pinned), Translation Free. K = 2.0
The end conditions in steel are either fixed or pinned.
The end condition (K) of a column affects its load carrying capcity. K is the variable that deals with end conditions concerning the slenderness ratio SR = Kl/r
Describe a Vault
A covering over an area that behaves like a series of adjacent Roman arches. Commonly constructed of masonry, the arches create a continuous structure, supported at its longitudinal edges. Like an arch, a vault needs lateral restraint at the spring line.
An overhang is supported by two steel rods, each 3/4” diameter. The tributary load from the overhang to teh two rods is 8,000 lbs.
What is the stress in each rod?
A - 9,091 psi
B - 18,182 psi
C - 2,800 psi
D - 4,400 psi
A - 9,091 psi
Since the radius of gyration of one rod is: r = d/2 = 0.75/2 = 0.375”
Then the area of each rod is A = πr2 = (3.142)(0.375)2 = 0.44 in2
Its share of the load is 8,000lbs/2 = 4,000lbs.
Using f = P/A then 4000/0.44 = 9,091 psi on each rod.
If these rods are A-36 steel, then the allowable tensile stress is FT = 22 ksi which is greater than 9.09 ksi and the rods are far being stressed to their limit.
Which of the following is NOT true regarding Dulles International Airport?
A - The building consist largely of concrete and glass.
B - It incorporates mobile lounges to accomodate the distance from the terminal to the planes.
C - The roof structure is an elongated catenary arch.
D - Its circular plan allows for direct radial access from the ticket counters to the gates.
D - Its circular plan allows for direct radial access from the ticket counters to the gates.
Designed by Eero Saarinen, it was built near Washington D.C. in 1964.
Although the plan was organized around the circulation, the building has a rectilinear footprint.
Lamella Roof
A framework for forming domed or arched surfaces, typically roof structures. It consists of two sets or parallel arches that intersect to form a grid in plan.
Advantages include:
Repetition of like elements and joint details, the ability to span great distances, can be made of wood, steel or concrete.
The italian engineer Pier Luigi Nervi is crdited with using this system extensively foir teh construction of airplane hangars
Name the strutural engineer who played a key role in the design of the Olympic Games complex in Munich.
Frei Otto
Completed in 1972, it is composed of a series of steel nets stretched between steel masts and anchored to the ground by steel cables. The roof structure is a high-tech PVC-coated polyester fabric tent that has inspired the use of tensile structures in archtectural design.
For the W shape section with two equal cover plates shown below, compute the Moment of Inertia about teh X-axis.
From the AISC manual, the proerties of a W16x57:
Actual depth d = 16.43”
Area:
A = 16.8 in2
IX = 758 in4
rX = 6.72”
Total area of the built up section: 16.8 + 2(8 x 1) = 32.8 in2
IX = IX of the W shape plus IX of the cover plate plus the transfer of IX of the cover plate to the new X-axis.
The distance from teh X-Axis of teh W16 to eth X-Axis of teh cover plate is
16.43/2 + 1/2 = 8.715”
Therefore:
IX = 758 + 2((1/12 x 8x 13) + 8(8.715)2)
IX = 758 in4 + 1216.55 in4 = 1974.55 in4
Find the tributary area for a 4” x 12” beam placed 4’ on center and spanning a distance of 20’
4’-0” x 20’-0” = 80 ft2
This area is equal to the beam span multiplied by beam spacing. It is the area of effective load that a structural member must carry.
With regard to an arch, what is thrust?
The horizontal force exerted by an arch that causes it to spread outward. This force is proportional to the load and the span, and inversly proportional to the rise.
To calculate, use the formula:
F = M / D
Where:
M = Moment of the Arch
D = the rise of the arch.
Can be resisted by supporting the arch with an adjoining arch, or by using steel tie-rods, a sufficient foundation or a shear wall.
For the beam below, how are the maximum moment and the reactions computed?
Maximum Moment = Pab/l at the load
Reactions:
L = (b/l) x P
R = (a/l) x P
Since b > a, R will be smaller than L (load is closer to L than to R).
It is important to think of L and R as being fractions of teh 25k load. L larger than R since teh 25k load is closer to L. So the 25k load breaks down into teh foolowing reactions:
L = (16/20) x 25k = 20k
R = (4/20) x 25k = 5k
L = 20k and R = 5k
Calculate the Reactions, Maximum Shear, and Maximum Bending Moment for each of the following loading conditions.
Waffle Slab
A type of two-way concrete slab normally used along with long spans and heavy loads.
Two perpendicular sets of ribs typically reinforced and cast in place using reusable square forms. The waffles around a column are filled solid to avoid two-way punching shear. To accomodate rectangular spaces ribs may be deeper in one direction or contain additional reinforcing. Often left exposed, this structural system tends to convey a sense of mass and rhythm.
Space Frames
A series of rigid frames that intersect each other in a grid pattern and are rigidly connected at their intersection points. This system works as a unit, similar to a two-way reinforced concrete slab. Space frames are used to span large, column free areas. They are statically indeterminate. A space frame is more efficient when it overhangs one bay in each direction.
What are the THREE equations of equilibrium with regard to any structural member?
1 - The sum of all vertical forces equal zero
2 - The sum of all horizontal forces equal zero
3 - The sum of all moments or the moment of all forces equal zero.
If these equations can be solved, the beam is staically determinate.
Note: The branch of mechanics that focuses on forces and equilibrium or bodies that are held motionless by forces acting upon them is known as statics. Where the resultant of all forces acting on a body os zero.
Describe different methods of attaching a structural spanning member to its supports.
Identify the components of this fillet weld.
A - Penetration: The depth of a weld from the surface of the base metal to the point at which the two metals cease to fuse.
B - Reinforcement: Additional material beyond the dimension of the throat.
C - Throat: In a fillet weld, it is the ditance from teh intersecting surfaces of the base metal perpendicular to the hypotenuse of an inscribed isosceles right triangle.
D - Size: The length of the leg of the inscribed isosceles right triangle. THis is the specified diemnsion, for example 3/16”
E - Root
F - Toe
Continuous Beam or Slab
A member that rests on three or more supports and is statically indeterminate. Maximum bending takes place over the first interior support. Negative moment occurs over the supports. Positive moment occurs between the supports.
Molecular diagram of a beam in deflection:
Identify the conditions at A, B, and C.
A - Compression: Shortens
B - Neutral Axis: Remains the same length
C - Tension: Elongates
The length of molecular bonds will change in deflection. The molecules resist this change in length and create an internal force which resists an external force. A deeper beam will have more molecules to create greater resistance to loads. Increasing the depth of a beam is an effective solution to accomodate larger loads or longer spans. The compression increases from zero at the Neutral Axis to a maximum (C) at the top of the beam. Likewise, Tension increases from zero at the N.A. to a maximum (T) at the bottom of teh beam.
The couple that is formed between Compression at the top and Tension at the bottom, separated by a couple arm equal to the depth of the beam, is what resists external moments.
Modulus of Elasticity (E)
A measure of the stiffness of a material, and its resistance to deformation. It is a ratio of stress to strain (deformation) and is unique to each material.
This stress/strain ratio was identified by Thomas Young (1773-1829) and was first published in 1807. He was also responsible, in part, for the decipherment of Egyptioan hieroglyphics. E is sometimes called Young’s Modulus.
Felix Candela is best known for what kind of structural design?
A - Suspension Bridges
B - High-rise Steel Frames
C - Long Low-cantilevered Floor Planes
D - Thin Concrete Roof Elements
D - Thin Concrete Roof Elements
Born in 1910, Candela’s roof structures incorporated cleverly ‘folded’ cast-in-place concrete plates in paraboloid , dome and saddle shapes. These folds increase the stiffness of the structure and act like trusses or beams.
Identify this type of arch.
Three-hinged Arch
An arch with hinges at each support and a third hing at the apex. Due to the third hinge, the structure is statically determinate, that is, the reactions can be found by using the equations of equilibrium. This type of arch allows for the thermal expansion and contradiction and uneven settling without bending derormation of the two arch members. A two-hinged arch, like continuous and fixed-end beams are statically indeterminate and require complex calculations to find the reactions. Both types of arches must resist outward thrust at the abutments. A simple method of resisting this thrust is by using a steel tie-rod. similarly, domes must resist thrust and this can be achieved by the use of a tension ring at the dome base. This may be seen at the base of the Pantheon dome, where a chain was added to prevent the dome spreading.
How is Lumber classified?
Nomenclature for calculating Steel and Timber Beams.
Section Modulus (S)
S = M/Fb
Used in beam design to determine the required property for the beam cross-section. S is equal to the maximum moment (M) divided by the maximum allowable bending stress (Fb). A measure of the bending capacity of the shape, not a rating of the material. Steel beams with a higher percentage of material in the flanges will have a larger value of S and will be able to resist greater bending. It is equal to the moment of inertia divided by the distance from the center of gravity to the extreme fiber.
For rectangular sections, Sx = IX/c = bd2/c
Section modulus is measured in in3.
Identify this diagram and the conditions at points a, b, c and d.
A Stress (y) / Strain (x) graph which is a graphic representation of a material’s ability to resist force and resulting deformation. This graph is different for different materials.
a - Elaatic Limit: The greatest unit stress that a material can resist without permanent deforamtion when the stres sis removed. Described by mathematician, architect and physicist Robert Hooke. Hooke’s Law of Physics states that stress is directly proportional to strain and remains constant up to the elastic limit. The slope (rise/run = stress/strain) of this diagram in the elastic limit is called the Modulus of Elasticity (E) and is a measure of a material’s resistance to deformation. Twice the force will produce twice the deformation and when the force (up to a material’s Elastic Limit) is removed, the material will return to original size and shape.
b - Yield Point: A point beyond the elastic limit, up to which a material deforms with only a small increase in force and after which a material will continue to deform with no increase in force. The deformation is permanent.
c - Ultimate Strength: This is the maximum unit stress of a material that occurs just at or before failure.
d - Rupture: Material fails.
A simple concrete beam represented below by a dashed line is replaced by a new beam. Which of the following statements is true with regard to the new beam?
A - the beam needs a substantial increase in the amount of reinforcing.
B - the beam now has a greater load carrying capacity.
C - the beam now has a shorter span capacity.
D - the beam now has a greater resistance to shear at the supports.
B - the beam now has a greater load carrying capacity.
Due to an increase in the effective depth and therefore also in section modulus in the new beam, it is now able to support a greater load , moment, and span a greater distance. Also with the increase in effective depth, the beam will have a greater moment of inertia and will this result in less deflection. The resistance to shear at the supports remains relatively unchanged, since the height and area of the beam at the supports appears to be unchanged.
Define the components of the following designations
1 - W10x112
2 - WT9x30
3 - HP10x57
4 - S12x50
5 - C5x9
6 - L5x3x1/2
7 - TS10x6x3/8
8 - 6” Ø: extra strong
Calculate the Maximum Bending Moment for the following simply supported beam. The beam has a uniformly distributed load of 500lbs/ft.
Using the formula M=wl2/8 or WL/8
Where:
w = 500 lbs/ft.
W= (500 lbs/ft.) x 12’ = 6000lbs.
Therefore:
M = (6000 x 12)/8 = 9000 ft.-lbs.
Identify the Roman arch.
Diagram D
Also called the a semicircular or round arch, the Romans were first to introduce the shape of a half circle. This offered convenient construction properties since each unit can be the same shape. They were commonly used to span modest distances and could be used to create vaulted space of 100’.
A is Parabolic arch, similar to a catenary arch.
B is a three-centered arch or basket arch.
C is a four-centered arch or Ogee arch.
Identify the structural system used in the following drawing
Panel Bracing or Staggered Truss
A vertically-oriented lateral load resistive system incorporated into the structure when additional wind or seismic bracing is required. It is achieved by stiffening alternate bays at alternate floors with panels or diagonal framing members.
Considered a structural irregularity by SEAOC, Structural Engineers Association of California, because of its “unusual or novel structural features.”
Identify these light framing connectors.
A - Framing Anchor
B- Truss or Joist Hanger
C- Gang Nail Plate Truss Connector (toothed plate)
Used in light frame wood construction, these metal plate connectors are typically fastened using short nails meant for 2” wood members. They serve to tie the members together and improve resistance to lateral and uplift loads.
All of the connectors shown are considered pins or hinges and do not restrain the joint against rotation.
Identify these common concrete masonry units and their characteristics.
A - Stretcher (3 core): unit most common for unreinforced construction.
B - Double stretcher: Most common for reinforced construction. Large cores with vertical steel bar and grout create internalize informed concrete columns.
C - Low Web Bond-Beam: Unit provides space for horizontal reinforcing bar and grout. Used to tie wall together at critical points or create a bond beam.
D - Channel Bond Beam or Lintel: Unit provides space for horizontal reinforcing bar. Used to create lintels or over openings.
E - Control Joint: used for making expansion or vertical shear type control joints in construction. Sealant is used between interlocking units.
F - End: Used where the end of the unit will be exposed.
G - Corner: half block used at ends of walls to create a running bond pattern.
Which diagram represents the deformation of this continuous beam loading diagram?
Diagram C
The continuity of the beam stiffens the loaded span by restraining the rotation that would normally occur at the ends of a simply supported beam. The beam behavior of the loaded span is similar to that of a fixed-end beam. The load causes bending and shear in the unloaded spans and is considered to be carried by the entire beam, not just the span in which the beam is loaded.
Compared to a simply supported beam with the same load and span, the continuous beam is subjected to less bending moment and therefore, less deflection.
If the beam below is subjected to uneven settlement, which diagram represents the appropriate reaction?
Diagram D
Since the beam ends are fixed and rotation is prevented, bending Stess will result. The point of inflection (POI) occurs at the mid span and the two beam halves react as though they are cantilevered and carrying loads at their tips.
Effects of uneven foundation settlement in continuous vs. simply-supported beams.
Continuous: Extreme fiber stresses change from compression on the top and tension on the bottom (positive bending), to tension on the top and compression on the bottom (negative bending). Bending stress is transferred from one bay to the next.
Simply-supported: The beam ends are hinged, the beam can adapt by rotating around the hinge. No additional stress is imposed on the beams and they remain straight, though tilted.
Metal decking
Common in steel frame construction. It serves as permanent formwork and tensile reinforcement for concrete floor and roof decks. Made from galvanized sheet steel, the corrugations increase the stiffness of the deck by forming concrete into one-way ribs. The spanning distance is largely a function of the gage of the steel and the depth and frequency of the corrugations. It can be used instead of temporary plank flooring during construction, and is usually puddle-welded to the beams.
Metal shear studs (Nelson studs) are sometimes welded to the top of the steel beams and protrude into the concrete. This integrates and strengthens the structure by developing shear resistance between the beam and the concrete. Shear studs improve the rigidity of the connection between the diaphragm and the supporting steel frame. In order to increase fire protection, the exposed metal deck is often covered by fire-resistive panels or sprayed-on material.
Identify the connections shown below.
1- a bolted beam-to-column, shear connection. It is a shear-only connection because the beam flanges are not rigidly connected to the column. Note the gap shown between the bottom flange of the beam and the column.
2- a welded beam-to-column, moment (rigid) connection. The beam flange welds transmit full flange strength to the column. The shear tab, welded to the column, and bolted to the beam web supports the beam until it is welded and offers permanent shear resistance. Electric Arc Welding is generally used in steel construction with the fillet weld being the most common type of weld.
A moment connection is one that can stabilize a frame against lateral forces without the use of diagonal bracing or shear walls.
Identify these beam failures
In a simply-supported beam with a uniformly distributed load, there are three possible, distinct tendencies to fail.
1 - vertical shear: critical at the support locations for short beams with small cross-sectional areas that are heavily loaded (especially if large load is concentrated near support).
2 - Bending: Occurs at the point of maximum moment or at the mid-span of the a uniformly loaded beam. Usually occurs with larger spans that are uniformly loaded.
3 - horizontal shear: This type of failure happens mostly in wood members where layers (growth rings) may slip past each other in a horizontal direction.
Wood and concrete are more prone to failure by shear stress than steel members. Shear stress is critical in the design of members with a small cross-sectional area, and those that have short spa sand carry heavy concentrated loads.
Wood Beam Integrity
Framing members must sometimes be notched, drilled, or cut to accomodate mechanical, electrical or plumbing equipment. However, it should be done in a way that will limit the impact on the member’s structural integrity.
Notching should not be done in the center 1/3 of the beam span and should have a depth < 1/6 of the beam depth.
Holes should not exceed 1/3 of the beam depth and should not be located within 2” of the top or bottom (as close as possible to the Neutral Axis). Holes should be located away from the beam end supports to minimize the exposure to shear and away from the midspan to minimize the exposure to large bending moments.
Name TWO examples of column footing failure.
1 - Two-way or Punching Shear: the column tends to punch through the footing.
2 - One-way flexural shear or diagonal tension: Considered ordinary beam shear, the two-way reinforcing in the tension face of the footing resists bending. Normally, if shear is a problem the footing is made thicker.
The footing generates stress in the soil mass directly under the footing where, for calculation purposes, the soil bearing capacity is considered to be a uniformly distributed constant reaction. This is the most common type of shallow foundation and is called an isolated pad footing, a type of spread footing. It is poured directly on the soil and the transfer of stress from the footing to the soil is through direct bearing pressure.
Identify these nailing methods
1 - Face Nailing: The strongest nailing method
2 - End Nailing: The weakest method. A nail is driven through one piece of wood into the end grainof the adjoining piece. WOrks best for holding members in alignment until additional framing or sheathing can strewngthen the connection.
3 - Toe Nailing: About 2/3 as strong as face nailing. Used when access is not available to end nailing.
Note: Blind nailing is a method of toe-nailing where the nail head is to be concealed by the adjacent piece of wood.
What parameters will govern the design of a combined footing?
This type of spread footing is used to support two or more, possibly several, closely spaced columns. Ideally, the footing will have such area and weight that the centroid of the footing will coincide with teh centroid of the coulmn loads plus the footing itself. HOwever, this is not necessary as long as the resulting eccentricity does not create an overstress in teh bearing soil. In addition, the column spacing and allowable soild bearing capacity will control the footing size.
Formulas for Common Beam Loads
Identify the shaded elements in the sketch below.
Cover Plates
These steel plates are welded to a steel wide flange beam to increase the load carrying capacity of the member. They are usually added to both the top and bottom flanges. Can be used to slightly minimize section depth where space is limited.
Identify the truss components below.
A - Diagonal web member
B - Top chord
C - Panel point (truss joint)
D - Bottom chord
E - Vertical web member
The top and bottom chords are analogous to beam flanges and are thus primarily responsible for bending stresses. Diagonals and verticals are analogous to the beam web, and are thus primarily responsible for shear stresses.
For the beam loaded as shown, what condition must be considered at point A?
At point ‘A’ the beam tends to lift off the support. The design of the connection must be sufficient to hold beam end ‘A’ on the support and foundation. Summing moments about point ‘B’ will show that reaction ‘A’ needs to be downward to provide a counter-clockwise moment to balance the clockwise moment created by force ‘P’ about point ‘B’. Thge downward reaction implies that it is a tie-down that must resist uplift at ‘A’.
Consider the two uniformly loaded beams shown below. How will their designs differ?
Assuming the three spans are equal in the two beams:
Beam 1: The continuous beam will develop a given set of moments and is statically indeterminate.
Beam 2: The location of the internal hinges will affect the moments in this beam and may result in a lower design moment. It is statically determinate. In this beam, the middle span is simply supported on the two overhanging end beams. The reaction from the middle span is a concentrated load onto the end bay and thus may generate more moment than the uniform load could generate on beam 1.
Two buildings of different heights are closely spaced. What affect might the taller building have on the snopw load of the shorter building.
The taller building will have a tendency to cause the snow to drift or accumulate on the shorter building when the two buildings are adjacent. Codes require the structure of the shorter building to account for this phenomenon. This loading tendency lessens as the spacing between the buildings gets larger and is eliminated as a code requrieemnt at about 20’.
Note: the right reaction in the sketch below is greater than the left due to additional snow accumulatiuon.
How is the maximum moment and maximum shear calculated in the uniformly loaded beam below?
For a simply supported, uniformly loaded beam the maximum moment at mid-span = wl2/8 or WL/8.
Maximum shear at each end = wl/2 = WL/2 which is equal to the reaction (R) at each end.
Where:
w = load per foot of span.
W = total uniform load
l = length of the span
Remember that the maximum shear is in lbs/kips and maximum moment is in lbs-ft. or kip-ft.
Flexural Strength
The ability of a beam to resist bending forces. It is determined by a material’s resistance to internal tension and compression forces. It is a critical factor in the design of any load bearing horizintal structural member that is loaded perpendicular (Normal) to its axis.
The drawing shows compression of the top fibers of the beam, and tension of the bottom fibers (with failure). This is positive flexure.
Draw the bedning Moment Diagram for each shear diagram below. Calculate the maximum moment for each.
Two cables are suspended as shown. What type of curve will the cables assume?
A - Circular
B - Parabolic
C - Catenary
D - Ellipsical
1 - C - Catenary
Cable 1 has a uniformly distributed load along its length. This type of load configuration would result from weight of the cable itself. This naturally draped shape forms a catenary and is evident in electrical transmission lines, for example.
2 - B - Parabolic
Cable 2 is uniformly loaded with respect to a horizontal projection, similar to that found in a suspension bridge deck. Note that this parabola is the shape of the moment curve for a uniformly loaded beam.
Both curves have similar configuration and a sag ratio of about 1/3 span, where sag is the vertical distance between the lowest point in the cable and the supports. In both curves the supports resist downward force as well as inward thrust. A cable is the structural opposite of an arch. The cable is always in tension while the arch is in compression. Neither system can handle much shear or bednding moment. While these forces will change in magnitude, the sag can be adjusted without changing the load by simply moving the supports closer together or further apart. The steeper the cable (or arch), the larger the vertical component of the reaction. The shallower the cable, the larger the horizontal component of the reaction.
What is the relationship of a froce to its slope, and its vertical and horizontal components?
What is the minimum section modulus for a steel beam that will carry the load shown?
Assume full lateral support and yield stress (Fy) = 36 ksi.
A - 295.77 in3
B - 448.76 in3
C - 271.13 in3
D - 282.46 in3
C - 271.13 in3
Moment is equal to the moment due to the evenly distributed load plus the moment due to the two concentrated loads
For evenly distrubted load:
M = WL/8 or wl2/8
For the concentrated loads:
M = P x a
where P = load and a = distance of load from teh supports.
(wl2/8) + (P x a)
Therefore:
(2 x 272/8)+(40x9) = 545.25 kip-ft
The allowable bending stress (Fb) is equal to 24 ksi for members with full lateral support. So the minimum section modulus capable of carrying the moment is
S = MMax/Fb = (542.5 kip-ft. x 12)/24 ksi = 271.13 in3
For design purposes, a fillet weld in section is considered to be a right isoseles triangle. Its specified size D is equal to teh length of one side of that triangle.
These welds are designed to limit the stress on what?
A -The leg
B - The throat
C - The chord
D - The angle
B - The throat
afc = right isosceles triangle
ab is perpendicular to fc, therefore: abc is also a right isosceles triangle.
ab (throat) = bc
According to the Pythagorian Theorem (ab)2 + (bc)2 = D2
Since ab = bc, then 2(ab)2 = D2 or (ab)2 = D2/2
Throat = ab = D/(sqrt 2) = .707D
For the truss shown,
1 - Calculate the force in members BC, CP, GK, HJ
2 - Calcualte the force in members AB, DN, ME, FL, GH
1 - The force in BC = CP = GK = HJ = 0
The method of joints allows us to examine the equilibrium of each joint independently.
For each joint ΣFx = 0 and ΣFy = 0
In these section drawings of reinforced concrete beams, name the item identified as x and what is its function?
Stirrups
These bent steel reinforcing bars, usually a #3 or #4 bar, are used in reinforced concrete construction. They are open or closed and are placed transversely in beams. They are placed at specified intervals throughout the member, most closely near columns or where diagonal tension is highest. They serve several purposes:
1 - They resist Shear where the stresses are greater than the capability of the concrete.
2 - They resist T_orsional (twisting) moments_ when present. Whenever possible, torsion will be designed out of the structure.
3 - The restrain any compression reinforcing from buckling.
4 - Although their true purpose is structural, they help hold the longitudinal reinforcing in place and maintain proper spacing during concrete placement.
Their usage is covered in ACI 318, the usual governing code.
For the three-hinged framing shown below, what are the vertical and horizontal reactions?
In a built-up cross section, the centroid is always located:
A - Midway between the top and bottom of the section
B - On the section itself
C - On an axis of symmetry, when one exists
D - Some place outside the area of the section
C - On an axis of symmetry, when one exists
Any axis of symmetry will always pass through the centroid.
The other answers could be correct, for example
A - W-Shape steel sections
B - Rectabgles
D - Channels and angles
Properties of common cross sections.
Define eccentricity in a steel column.
Eccentricity (e) is the perpendicular distance from the neutral axis of a steel column to the Line of Action (L.O.A.) of the applied load or reaction. The eccentricity can be about the x-x or y-y axis of the column.
B1 creates moment about the y-y axis
B2 creates moment about the x-x axis
Thus, the steel column has to carry combined loading (axial and bending).
Calculate the stress in the throat of the 3/16” fillet weld diagrammed below.
In a 3/16” fillet weld, the throat dimension is:
(3/16) x 0.707
Since the length of the two welds combined is 4” x 2 = 8” then:
3/16 x 0.707 x 8 = 1.605 in2
The stress in the throat:
Stress = Load/Area = (10,000)/1.0605in2 = 9,429.5 psi
Friction-type Shear Connections
A bolted connection between two structural members that transfers force from one member to the other through frictional stresses between the contact surfaces of the members. No bearing action occurs because the parts are assumed not to slip.
Given a uniformly loaded, simply-supported beam, the result of shifting the supports toward the center of the span is:
A - a decrease in beam efficiency.
B - an increase in beam efficiency
C - a decrease in shear
D - an increase in deflection
B - an increase in beam efficiency
Shifting the supports toward the center of the span creates two overhanging ends that balance the load between the supports. This reduces the bending moment and the deflection at midspan and reverses the curvature of the beam near the supports.
Slenderness Ratio (SR) - Wood
For simple solid wood columns, the SR is equal to L/d, where L= the unbraced length (laterally supported) and d is the column’s least sectional dimension. The SR is used to determine the maximum allowable unit stress for the column (Fc’) for compression parallel to the grain, and is the most critical consideration in column design. The taller the unbraced length (L), the greater the slenderness ratio, the less Fc’. Similarly, the smaller the least dimension (d), the greater the slenderness ratio and less Fc’.
What is the most common and most economical type of spread footing?
A - Combined Footing
B - Mat Footing
C - Wall Footing
D - Pile Footing
C - Wall Footing
Generally classified as a shallow bearing foundation. It supports vertical loads and consists of a continuous strip of concrete, typically reinforced longitudinally, and transversally, rectangular in cross-section and placed under a foundation wall. Its continuous nature allows it to distribute the building load over a broad area and span over isolated areas of weaker soil. A keyed joint is commonly used to strengthen the connection between the foundation wall and the footing.
In Calculating Shear in wood beams, which loads may be neglected?
Loads located at a distance (d) from either support that are equal or less than the depth (d) of the beam.
Calculate the Left and Right reactions for the beam shown below
A - L = 42k, R = 42k
B - L= 20k, R = 52k
C - L= 40k, R = 32k
D - L = 30k, R = 54k
C - L= 40k, R = 32k
Resolve the 30k load at point C into vertical and horizontal components.
Cv = 3/5 x 30k = 18k
Ch = 4/5 x 30k = 24k
The pin/hinge connection has two reactions, H and L and the roller has one reaction, R. Thus:
Without further calculation, we know that L should be larger than R since 30k at point B is greater than 18k at point C. So the only possible answer choice is C. If calculation is necessary, isolate asymmetrical loads from symmentrical loads as shown.
The 30k load at point B exceeds the 18k load at point C by 12k, otherwise the load is symmetrical.
L = L1 + L2 = 30k + 10k = 40k
R = R1 + R2 = 30k + 2k = 32k
Which of the following causes the greatest resistance to bending in a simply supported beam?
A - Columns
B - Beam Depth
C - A high slenderness ratio
D - Continuous Load
B - Beam Depth
An increase in beam depth will reduce deflection.
A - Keystone
B - Voussoir
C - Springers
Though each wedge-shaped unit in an arch or vault os known as a voussoir, the keystone and springer are further defoned.
Keystone: The center stone or masonry unit at the apex of an arch. Often decorated, embelished or exaggerated in size, no true arching action occurs until this unit is in place.
Springer: The lower-most voussoir, located where teh vertical support ends and the curve of the arch begins.
During construction, a temporary formwork called centering is used to support the vault or arch until the structure is self-supporting.
Positive Bending Moment in Beams
In a concrete column, failure may occur at the point of maximum stress.
With respect to the direction of the applied force, at what angle will shear stress occur?
A - 30o
B - 45o
C - 60o
D - 90o
Net Section
C - 168.75 in3
Moment M = WL/8 or wl2/8
3(30)2/8 = 337.5 kip-ft.
If full lateral support of the compression flange is provided, then for A-36 steel. Fb = 24 ksi. To find the minimum Section Modulus,
Sx = MMax/Fb = 337.5/24 x 12 = 168.75in3
Dimension D
The distance from teh compressive face of the beam to teh centroid of teh steel reinforcing. This is the dimension used in beam design calculations.
Dimension A is called cover, and is goverened by building codes . It ranges from 3/4” (slabs) to 3” (foundations) depending on the type of member and its exposure to soil or weather. A higher fire rating can be achieved by increasing cover.
Dimension B is the width of the concrete.
Dimension T is the location of the Tension Stress
Dimension C is the location of the Neutral Axis.
Dimension H is the overall depth of the beam. This is the dimension, in addition to the woidth (B), that is used to calculate the weight of a concrete member.
In a continuous beam, the top face chnages from compression to tension over the supports. This requires reinforcing at the top of the beam as well.
Since the load is closer to the left end of the beam, the Left reaction is greater than the Right.
L = (P x b)/l x 60kips = 42.86 kips
R = (P x a)/l x 60kips = 17.14 kips
Maximum moment:
(P x a x b)/l = (60 x 8 x 10)/28 = 342.86 kip-ft.
Since the compression flange has full lateral support:
Fb = 24ksi
Fb = M/S ⇒ S = M/Fb = (342.86 x 12)/24 = 171.43 in3
Lintel
A simple beam with a concentrated load at the center of the span.
P = the concentrated load
L = the length of teh span
P/2 =- each reaction
L/2 = Shear (v) passes through zero at center span where Bending Moment (M) is at its maximum.
To solve for maximum bending moment at mid-span, calculate the sum of the areas in the shear diagram to the left of the mid-span
Since M = PL/4
M = (9 x 12)/4 = 108/4 = 27 kip-ft.
Reactions (R)
What is the function of a washer in a bolted connection?
Describe the characteristics of a folded-plate structure.
In wood column design, which end condition is always used?
Compare the variation in force for the top chord, bottom chord, and web members for:
1 - A Howe Truss
2 - A Pratt Truss
Both are parallel chord trusses and are simply supported at their ends. The orientation of the web members in each is different.
What is a Balanced Condition according to the Ultimate Design Method for concrete members?
Refers essentially to the connections in a structural framework. These connections are capable of resisting any significant rotation of one member about the other. They include moment connections or moment-resisting connections that transfer bending between the joined members. These frames resist both lateral and vertical loads and are statically indeterminate structures. If the frame exists in a single-plane two-dimensional column-beam construction, it is called a bent. Commonly a welded connection. A rigid frame is a misnomer, since this construction generally produces a relatively flexible internal resistive system compared to the stiffness of a shear wall or a braced frame for example.
The phenomenon where both the axial force of tension or compression, and bending moment occur simultaneously at the same point in a cross-section of a structural member. This condition occurs with eccentrically loaded columns and may lead to P-Delta type failures.
The symbol is used with a horizontal reference line connected to an arrowhead line that points to the location of the weld. The symbol is placed above the reference line if the weld is on the side of the member away from the arrow, and below the line if the weld is on the same side. If it is to be welded on both sides, the symbol is repeated above and below the line.
The example indicates a 3/16” near-side fillet weld 2” long and 5” on center to be done in the field.
Calculate MAximum Shear (determines minimum Area), and calculate Maximum Bending MOment (determines minimum Section Modulus).
W = wL = 100lbs/ft x 16 ft = 1600 lbs.
Vmax = W/2 = 1600/2 = 800 lbs.
Mmax = WL/8 = wl2/8 = (100 x 162)/8 = 3,200 lbs-ft.
Shear Fv = 3Vmax/2A ⇒ Amin = 3Vmax/2Fv = (3 x 800)/(2 x 95) = 17.63 in2
Bending Fb = Mmax/S ⇒ Smin = Mmax/Fb = (3200 x 12)/1500 = 25.6 in3
In solving for reactions (R), a uniformly distributed load can be calculated as if it had what type of loading diagram?
Formula Chart for Beam Calculations
Stress
D - Vierendeel
It incorporates no triangulation or diagonal web members but relies solely on the shear and bending resistance of its components and the stiffness of its joints. The joints are fixed and act like a rigid frame in resisting loads. It requires more material than a triangulated member with the same span-to-depth ratio. It is often used for bridges and as deep support beams when clear openings are required in the bays.
Under the same load, a shorter truss depth would require larger member sizes and would experience larger member deformations.
A Needle Beam
It is a temporary cross-beam used to support an existing wall or floor during repair or underpinning work. Needle beams are typically made of timber or steel. One end of the beam is supported at grade. The other end of the beam is supported by a jack. This process is called needling.
What are the FOUR methods used to determine axial forces in a truss member?
How do forces exerted by soil act upon a retaining wall?
The point of inflection or point of contraflexure. It indicates the points of change in curvature of the deflected beam. The points of zero moment or zero bending stress, where the moment diagram changes sign from positive to negative or vice-versa and passes through zero.
These points are particulalry significant for reinforced concrete beams since they indicate where the reinforcing needs to be reversed. By definition, positive moment is when the top of a beam is in compression and the bottom is in tension. This happens between the supports, and the rebar will be placed on the tension side (bottom). The negative moment at the supports signifies that the rebar needs to be placed at the top (at the supports the tension is at the top of the beam).
Flitch Beam
What is a mechanical couple?
Poisson’s Ratio
