Beams & Columns

Question 1

What is the section modulus?

Equation?

Answer 1

The ratio of the beam’s moment of inertia to extreme fiber (the distance from the neutral axis to the outmost part of the section)

S = I/y
where I = moment of intertia
y = distance from the neutral axis to the extreme fiber

Question 2

What does statically determinate mean? What are 3 examples of statically determinate beams?

Answer 2

statically determinate = reactions can be found using equations of equilibrium (sum of all forces = 0). These types of beams have ends that are free to rotate as the load is applied.

1. simply supported
2. overhanging
3. continuous (extra support between end supports)

Question 3

What does statically indeterminate mean? What are 2 examples of statically indeterminate beams?

Answer 3

statically indeterminate = need more complex equations to find reactions. These types of beams have one or both sides restrained against rotation. The ARE exam focuses primarily on statically determinate situations.

1. cantilevered
2. fixed-end

Question 4

A shear diagram provides 2 important pieces of information:

Answer 4

1. Where the shear is maximum

2. Where the shear is zero = the point where bending moment is greatest and the beam has the greatest tendency to fail

Question 5

A moment diagram provides 4 important pieces of information:

Answer 5

1. The max moment occurs where the shear diagram passes through zero
2. When the shear diagram is a constant horizontal line between two concentrated loads or reactions, the moment diagram is a straight, constant sloped line.
3. Where the shear changes abruptly (as shown by a vertical line), the slope of the line representing moment also change abruptly
4. Where the moment crosses the neutral axis = inflection point = where reinforcing rods in concrete beams are bent to change from carrying positive moment to negative moment

Question 6

What are 4 things you need to know to find moment from a shear diagram?

Answer 6

1. The area of the shear diagram between two points = the change in moment between the same two points
2. A sloped shear line will result in parabolic moment line
3. A flat/horizontal shear line will result in a diagonal moment line
4. A flat/vertical shear line will result in a change in slope in moment lines (aka a max pos or max min value)
   i. e. = Where the shear = 0 will be max positive or negative moment

Question 7

What is deflection? What is allowable deflection?

Answer 7

Deflection = the change in vertical position of a beam due to a load

Allowable deflection = limited by building code requirements or practical requirements

Question 8

The amount of deflection depends on:

Answer 8

1. The load
2. Beam length
3. Moment of inertia of the beam
4. The beam’s modulus of elasticity

Question 9

What is the rule of thumb for deflection due to:
live load?
total load?

Answer 9

Deflection due to live load is typ limited to 1/360 of the beam’s span

Deflection due to to total load is typ limited to 1/240 of the beam’s span

Question 10

Moment, shear, and deflection for common beams are provided on the ARE exam resources. What is the symbol for each?

Answer 10

moment = M
shear = V
deflection = delta

Question 11

How do you find shear at a point on a beam? Moment?

Answer 11

Shear: take a point along the beam, and add up forces to the left of it.
up = positive force
down = negative force

Moment: take a point along the beam, and add up all (the forces x distance to the point) to the left of the point
clockwise = positive moment
counterclockwise = negative moment

Question 12

What is the radius of gyration (for columns)?

Answer 12

a convenient way to combine the properties of area and moment of inertia that is useful in column design
r = sqrt (I/A)

Question 13

What is the slenderness ratio?

Answer 13

the most important factor in column design. It gives the max stress a column can resist without buckling

slenderness ratio = L/r
where
L = length of column in inches
r = radius of gyration

Question 14

What are the 3 Categories of Columns

Answer 14

1. Short compressive members: F= P/A aka buckling is of most concern
2. Intermediate columns: various formulas depending on conditions
3. Slender columns: L/r aka slenderness ratio is of most concern

Question 15

What are the 4 possible end conditions for a column?

Answer 15

End fixed against rotation and translation
End free to rotate but with translation fixed
End free to translate but rotation fixed
End free to rotate and translate