Deflection Flashcards
What roof top phenomena, which can lead to dangerous
deflections
Ponding
if w is in PLF and L is in FT, what is the conversion factor when E is in PSI and I is in IN4?
1728 in3/ft3
Cantilevered beams fixed end
Moment = max Slope = 0 Deflection = 0
Cantilever beam free end
Moment = 0 Slope = max Deflection = max
Where does max deflection occur in a all simple beams
At the point of zero slope
Three factors that impact structural member stiffness
Material stiffness (E = elastic modulus) Sectional stiffness (I = moment of inertia) Beam length (L)
Equation for deflection (delta symbol)
Delta = (PL^3)/(48E*I)
P=force
L=length
E=elastic modulus
I=moment of Inertia
What is the largest roof deflection due to DL+LL recommended by the International Building Code?
L/120
What is the most commonly used limit for floor live load deflections?
Should not exceed L/360
The deflection limit of L/360 was originally determined based on the serviceability requirements of what material?
cracking of plaster ceilings. It was determined that plaster ceilings crack with a deflection larger than 1/360 of the span.
Code limits on deflection in beams are primarily performed to anticipate which type of structural problems?
Serviceability - It refers to conditions other than the building strength that render the buildings unusable. Serviceability limit state design of structures includes factors such as durability, overall stability, fire resistance, deflection, cracking and excessive vibration.
Mathematical sequence of diagrams by integration
Load diagram Shear diagram Moment diagram Slope diagram Deflection diagram
In a simply supported, symmetrically loaded beam, where does max slope occur
At the ends where the supports are (equal and opposite)
What values need to be multiplied with the areas of the moment diagram in order to calculate the angle of the elastic curve (in radians)?
1/(EI)
The inverse of the elastic modulus multiplied by the moment of intertia
Slope of beam is a measure of …
Angle in radians of the tangent to the elastic curve
What is the slope of the elastic curve at a fixed end condition
Slope is zero
For a symmetric, simple span beam using the diagram method, what observation about the slope diagram helps to find the point of maximum deflection?
Slope is always zero at center line
Can the diagram method of analysis be used to determine the value of the deflection for a simply supported beam that is not symmetrically loaded?
Yes, although a solution requires some additional work because the point of zero slope cannot be assumed to be at the midspan of the beam.
Of the parameter of deflection, which has the greatest effect when changed
Length of beam
For simple span beams using the diagram method, what observations about the slope diagram can help in finding the point of maximum deflection?
The positive and negative areas of the diagram will be equal. The point between the left and right parts of diagram will be zero, and will be at the point of maximum deflection.
When using superposition of equations to find the maximum deflection of an asymmetrically loaded beam, what must be observed regarding deflection location?
The location of the maximum deflection of each case is not the same as the combined case.
Code limits on deflection of beam vary according to what
Application (floor, roof, Dead load, live load)
