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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 lbfin Nmm
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.

 

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