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### Frame Deflections Left Vertical member guided horizontally, right end pinned equations and calculator

Beam Deflection and Stress Equation and Calculators

Frame Deflections with Concentrated Load on the Horizontal Member Equations and Calculator. Left vertical member guided horizontally, right end pinned.

General Designations

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Since ψA = 0 and HA = 0

MA = LPM / AMM

δHA = AHM MA - LPH

General reaction and deformation expressions with right end pinned

Where:

Reaction loads and moments VA and VB, and HB can be evaluated from equilibrium equations after calculating HA and MA.

Where:

Δo = Displacement (in, mm),
W = Load or Force (lbsf, N),
w = Unit Load or force per unit length (lbs/in2, N/mm2),
Mo = Applied couple (moment) ( lbs-in, N-mm),
θo = Externally created angular displacement (radians),
Δo, = Externally created concentrated lateral displacement (in, mm),
T1 - T2 = Uniform temperature rise (°F),
To = Average Temperature (deg °F),
γ = Temperature coefficient of expansion [ µinch/(in. °F), µmm/(mm. °F) ],
T1, T2 = Temperature on outside and inside respectively (degrees),
HA, HB = 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