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Frame Deflections Concentrated Lateral Displacement Applied Right Vertical Member Equations and Calculator

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Frame Deflections with Concentrated Lateral Displacement Applied Right Vertical Member Equations and Calculator.

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Frame Deflections with Concentrated Lateral Displacement Applied Applied to Right Vertical Member Calculator:

General reaction and deformation expressions with right  and left ends pinned

Horizontal Deflection at A:

Reaction locations are pinned therefore, the displacements = 0 = δ_HA

Angular Rotation at A:

Where:

Loading Terms LP_H and LP_M are given below.
Reaction loads and moments V_A and V_B, and H_B can be evaluated from equilibrium equations after calculating H_A and M_A.

LP_h = Δ_o ( -1 ); Δ_o can also be an increase in length l_3.

LP_m = 0

Reaction locations are pinned therefore, the Moments = 0 = M_A = M_B

Where:

Δ_o = Displacement (in, mm),
θ_o = Angular Displacement (radians),
W = Load or Force (lbsf, N),
w = Unit Load or force per unit length (lbs/in², N/mm²)
M_o = Applied couple (moment) ( lbs-in, N-mm),
θ_o = Externally created angular displacement (radians),
Δ_o, = Externally created concentrated lateral displacement (in, mm),
T - T_o = Uniform temperature rise (Deg.),
T₁, T₂ = Temperature on outside and inside respectively (degrees),
H_A, H_B = Horizontal end reaction moments at the left and right, respectively, and are positive clockwise (lbs, N),
I₁, I₂, and I₃ = Respective area moments of inertia for bending in the plane of the frame for the three members (in⁴, mm⁴),
E₁, E₂, and E₃ = Respective moduli of elasticity (lb/in², Pa) Related: Modulus of Elasticity, Yield Strength;
γ1, γ2, and γ3 = Respective temperature coefficients of expansions unit strain per. degree ( in/in/°F, mm/mm/°C),
l₁, l₂, l₃ = Member lengths respectively (in, mm),

References:

Roark's Formulas for Stress and Strain