Related Resources: calculators

Uniform Temperature Differential Frame Deflections Equations and Calculator

Beam Deflection and Stress Equation and Calculators

Frame Deflections with Uniform Temperature Differential Between Outside and Inside Equations and Calculator.

Loading Configuration

General Designations

ALL calculators require a Premium Membership

Preview

Frame Deflections with Uniform temperature Rise 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.

Note: t_`; t₂; and t₃ are beam thicknesses from inside to outside

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),
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