Two Member Frame - Fixed/Free Free End Vertical Point Load
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Two Member Frame - Fixed/Free Free End Vertical Point Load formulas
Support Reaction |
RA=P |
HA=0 |
Bending Moment |
Mmax(atpointsAandB)=PL |
Deflection |
ΔCx=PLh22λI |
ΔCy=PL23λI(L+3h) |
Slope |
θC=PL2λI(L+2h) |
Where:
Units | English | Metric |
Δ = deflection or deformation | in | mm |
h = height of frame | in | mm |
H = horizontal reaction load at bearing point | lbf | N |
Ih = horizontal member second moment of area (moment of inertia) | in4 | mm4 |
Iv = vertical member second moment of area (moment of inertia) | in4 | mm4 |
M = maximum bending moment | lbf−in | N−mm |
λ (Greek symbol lambda) = modulus of elasticity | lbfin2 | Pa |
A,B,C = point of intrest on frame | - | - |
θ = slope of member | rad | rad |
L = span length under consideration | in | mm |
P = total concentrated load | lbf | N |
R = vertical reaction load at bearing point | lbf | N |
diagrams
- Bending moment diagram (BMD) - Used to determine the bending moment at a given point of a structural element. The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
- Free body diagram (FBD) - Used to visualize the applied forces, moments, and resulting reactions on a structure in a given condition.
- Shear force diagram (SFD) - Used to determine the shear force at a given point of a structural element. The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
- Uniformly distributed load (UDL) - A load that is distributed evenly across the entire length of the support area.