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Distributed Load Elastic Frame Deflection Equation and Calculator

Beam Deflection and Stress Equation and Calculators

Distributed Load on the Horizontal Member Elastic Frame Deflections Equations and Calculator

Distributed Load on the Horizontal Member Elastic Frame Equations and Calculator
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General Elastic Frame Designations
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Distributed Load on the Horizontal Member Elastic Frame Deflections Calculator:

General reaction and deformation expressions with right and left ends pinned

Horizontal Deflection at A:
Horizontal Deflection at A:

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

Angular Rotation at A:
Angular Rotation at A:

Where:

Concentrated Load on the Horizontal Member Elastic Frame

Concentrated Load on the Horizontal Member Elastic Frame

Concentrated Load on the Horizontal Member Elastic Frame

Concentrated Load on the Horizontal Member Elastic Frame

Lph

Lpm

Reaction locations are pinned therefore, the Moments = 0 = MA = MB

Where:

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),
T - To = Uniform temperature rise (Deg.),
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

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