What is the section modulus?
Equation?
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
What does statically determinate mean? What are 3 examples of statically determinate beams?
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.
- simply supported
- overhanging
- continuous (extra support between end supports)
What does statically indeterminate mean? What are 2 examples of statically indeterminate beams?
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.
- cantilevered
- fixed-end
A shear diagram provides 2 important pieces of information:
- 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
A moment diagram provides 4 important pieces of information:
- The max moment occurs where the shear diagram passes through zero
- When the shear diagram is a constant horizontal line between two concentrated loads or reactions, the moment diagram is a straight, constant sloped line.
- Where the shear changes abruptly (as shown by a vertical line), the slope of the line representing moment also change abruptly
- 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
What are 4 things you need to know to find moment from a shear diagram?
- The area of the shear diagram between two points = the change in moment between the same two points
- A sloped shear line will result in parabolic moment line
- A flat/horizontal shear line will result in a diagonal moment line
- 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
What is deflection? What is allowable deflection?
Deflection = the change in vertical position of a beam due to a load
Allowable deflection = limited by building code requirements or practical requirements
The amount of deflection depends on:
- The load
- Beam length
- Moment of inertia of the beam
- The beam’s modulus of elasticity
What is the rule of thumb for deflection due to:
live load?
total load?
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
Moment, shear, and deflection for common beams are provided on the ARE exam resources. What is the symbol for each?
moment = M shear = V deflection = delta
How do you find shear at a point on a beam? Moment?
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
What is the radius of gyration (for columns)?
a convenient way to combine the properties of area and moment of inertia that is useful in column design
r = sqrt (I/A)
What is the slenderness ratio?
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
What are the 3 Categories of Columns
- Short compressive members: F= P/A aka buckling is of most concern
- Intermediate columns: various formulas depending on conditions
- Slender columns: L/r aka slenderness ratio is of most concern
What are the 4 possible end conditions for a column?
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
