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Concentrated Moment Left Vertical Member 8 Deflections Equation and Calculator

Beam Deflection and Stress Equation and Calculators

Reaction and deflection formulas for in-plane loading of elastic frame.

Concentrated Moment on the Left Vertical Member Elastic Frame Deflection Left Vertical Member Guided Horizontally, Right End Pinned Equation and Calculator.

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Frame Deflections with Concentrated Moment Calculator:

Since ψ_A = 0 and H_A = 0

M_A = LP_M / A_MM = Moment (Couple) at Left Node A

δ_HA = A_HM M_A - LP_H = Horizontal Deflection at Left Node 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.

Note: Δ_o could also be an increase in the length l₁ or a decrease in the length l₂.

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_A = Couple (moment) ( lbs-in, N-mm),
M_o = Couple (moment) ( lbs-in, N-mm),
θ_o = Externally created angular displacement (radians),
Δ_o, = Externally created concentrated lateral displacement (in, mm),
T₁ - T₂ = Uniform temperature rise (°F),
T_o = Average Temperature (deg °F),
γ = Temperature coefficient of expansion [ µinch/(in. °F), µmm/(mm. °F) ],
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, Seventh Edition