Project Development And Documentation Flashcards
Statics
structures in equilibrium; sum of all forces and moments = 0
If forces are in equilibrium
Structure is considered statically determinate, which allows it to be assessed with simpler methods
Free Body Diagrams
Force magnitude depicted as vector lengths
Force direction depicted as a vector and angles
The free body diagram allows for a proportional and graphical representation of the forces acting on a component. The resultant or reactionary force direction and magnitude can be determined by directly measuring the resultants
collinear forces: added together
Coplanar forces: forces in the same plane
concurrent forces: pass through the same point, but not necessarily in the same direction
Nonconcurrent forces: forces do not pass through a shared point
reaction: force acting at supports int eh opposite direction of loads that keeps a component in equilibrium
Specialty loads
Loads such as those from HVAC equipment, a bathtub full of water, or a large suspended piece of artwork may require careful consideration for the particular area that the component is located in
Misc Loads
Loads such as wall-mounted shelving, cabinets, light fixtures, audio-visual systems, etc…
structural shapes
depth over width for increasing capacity
the center of a beam experiences the least amount of stress or strain; the center is considered the neutral axis. Placing more material at the outer ends of the beam (the top and bottom) is the most efficient use of material and weight since the material is acting where it is needed most, at the ares of most stress and strain. This is the reason why steel W sections are shaped the way they areL a slender wall at the neutral axis with maximum material at the extreme ends of teh section
Generally, beams mainly serve to handle loads placed on them vertically, Columns often must withstand lateral and direct axial loads. For these reasons beams are typically lighter and deeper and columns tend to be more of a square shape.
The Section Modulus, Moment of inertia and radius of Gyration describe the shape of a structural component
Material structural properties
the tensile strength, compressive strength, and modulus f elasticity (E) describe the material properties
Stress
Stress = Internal resistance to an external force
Tension: Pulling force (elongation and tearing)
Compression: Pushing force (crushing and buckling)
Shear: ripping or sliding force
Bending:
Stress: = force / area The nunit for stress is typically psi, ksi, or psf
Strain
Strain: deformation of a material (ratio of material change in length to original length)
Elastic limit: each material has an associated elastic limit that, when deformed due to a stress, the material will still return to the form and size when the load is removed
Inelastic Limit: material is loaded beyond the yield point when the material will deform permanently under the load, but not break. Also known as the plasticity of the material
Ultimate strength: Failure of the material, breakage
Design should work well within the elastic limit
Modulus of Elasticity (E)
Modulus of Elasticity (E) = ratio of stress to strain; E = stress/strain. Represents a material’s “stiffness” or its ability to withstand elastic deformation. “E” is unique to each material and is not based on the shape of a material
Once a material reaches its yield point, it is no longer in its elastic region - meaning, the material will no longer return to its original shape or size, but will begin to deform permanently. “E” does not apply to materials once they are in an inelastic state
* Units are typically psi (pounds per square inch)
Modulus of elasticity of these construction materials:
Brass - 100 - 125 GPa
Aluminum - 69 GPa
Concrete, High Strength – 30 GPa
Douglas fir wood – 13 GPa
Section Modulus
• Section Modulus = ratio of Moment of Inertia to the extreme fiber of the material shape from the neutral axis
• S = bd2/6 for square or rectangular sections
• Section Modulus directly related to the geometry, or shape of a material
Section Modulus: S=M/Fb or S=bd2/6 or S=l/c c = distance from neutral axis to extreme
fiber, M = moment, Fb = allowable extreme bending fiber of a material, b = width of material,
d = depth of material
Moment of Inertia (l)
Moment of Inertia (l) = stiffness of the cross-section of the shape
Relates the material’s shape and material distribution to an axis in section (typically the neutral axis
The maximum bending stress is at the top and bottom of beams; the more material at these points, the less the stress per unit area. Hence, the shape and efficiency of shapes such as steel W-sections. The more material at the maximum stresses, the more
“stiffness” that shape gives to resisting the forces
| = bd*/12 for square and rectangular sections
Bending and Deflection
Bending and Deflection
Bending: the tension and compression occurring in a structural member (think beam) that causes it to bend. Checking for bending is one of the most basic and common structural checks. If a beam is loaded and bends downward toward the center, the top of the beam is getting compressed, while the bottom is in tension because of the
“spreading” motion. If a beam is continuous over multiple support points, the beam may actually begin to deflect upward at the support points
Deflection: is the “sag” or change in position of a structural member. This is important to check so that deflection does not produce unwanted effects such as cracks in materials, visual unpleasantness, development of unwanted slopes, or cause pressures on materials not meant to be under load, like windows and doors
Whereas a beam, floor joist, or girder may be of adequate strength to support the load, the deflection may impact the serviceability or function of the system. For example, a slight flutter or “bounce” in a floor when walking can potentially be a failure in serviceability where an uncomfortable situation is created by lack of deflection control
Radius of gyration (r)
Radius of gyration (r) = column properties of Area and Moment of Inertia
Unless perfectly symmetrical, a column will have a weak and strong axis; failure in buckling will happen at the weak axis first (think W-section)
Effective length
Effective length = the total unsupported length of a column (L)
Typically adjusted with a K-value
> Both ends fixed, k = 0.5
• One end fixed, one end pinned, k = 0.7
> Both ends pinned, k = 1.0
> One end free, one end fixed, k = 2.0
Slenderness ratio =
Slenderness ratio = L/r
Associated with columns. The higher the ratio, the more prone the column is to buckling The taller the column, the more prone it is to failure in buckling, short columns typically fail upon surpassing the allowable stress of a material; P=F ÷ A
Basic Formulas and Applications
Basic Formulas and Applications
P= F=A ; P= pressure (stress) F = force A = area
• A common application may be for sizing a spread footing with a column supporting a certain floor area
Spread footing
Sizing spread footing example: by rearranging the formula above, you get A= + P; Area
of footing = Total Load + Allowable soil bearing pressure
Example: Column load supported by a concrete footing is 25,000 #. The allowable soil bearing capacity beneath the footings is 2,500 #/sf
•Area of footing required to not exceed the allowable soil capacity. Area =
25,000 # / 2,500 #/sf = 10sf footing required. A 3’-3” x 3’-3” will provide the
required surface area
The allowable bearing capacity is just one of the checks required to design a footing. For example, if the column is exerting a lateral load, then the sliding capacity of the footing may have to be checked as well as the potential uneven distribution of pressure across the footprint of the footing onto the soil
Strain
Strain: €=e/L (where e= change in length, L= total length of member)
Yield point
Yield point: the point where any more stress imposed on the material would cause the material to deform
Shear force
Shear force: V=wL/2 (where V=shear stress, w=uniform load on member, L=length of member).
By dividing in two, this gives the amount of shear force at each of the member, such as a beam based on a uniform load
Connections
Connections: Where there are 4 or more reactions, a structural member will be considered indeterminate
Pinned connection = resists X & Y load directions
• Roller connection = resists Y
• Fixed connection = resists X, Y, & Moment
• Candidate must understand how to find reactions for a beam
A reaction is the upward force at the beam supports resisting the downward forces
• Candidate must understand moment diagrams and how to find the moment of a simple beam
-Moment = rotation about a point caused by a force
• Moment is the Force multiplied by the Distance from point under consideration
Moment (M) = Force (P) x Distance (d)
• Resisting moment is the internal moment opposing the bending moment
• Neutral axis is the centerline of a structural member where no bending stresses occur
Halving the span or doubling the width of a beam…
Halving the span or doubling the width of a beam reduces the stresses by half. Doubling the depth of a beam reduces the stresses by a factor of 4
Kern area
° Kern area = is a central area on a column or foundation. If load resultants remain within the kern area, then the compressive loads will not develop a tensile stress. If a load or combination of loads causes the reaction to result outside of the kern area, the element will develop a tensile stress that must be resolved. Reactions outside of the kern area on a footing will indicate that there is unequal weight distribution or footing is not contacting the subbase at all locations