**Related Resources: calculators**

### Concentrated Angular Displacement Left Vertical Member 9 Deflections Equation and Calculator

**Beam Deflection and Stress Equation and Calculators**

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

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

Loading Configuration

General Designations

ALL calculators require a *Premium Membership*

Preview

Frame Deflections with Concentrated Angular Displacement 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 *l _{1}* or a decrease in the length

*l*.

_{2}LP_{H} = θ_{o} (a)

LP_{M} = 0

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/in^{2}, N/mm^{2}),

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),

T_{1} - T_{2} = Uniform temperature rise (°F),

T_{o} = Average Temperature (deg °F),

γ = Temperature coefficient of expansion [ µinch/(in. °F), µmm/(mm. °F) ],

T_{1}, T_{2} = 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),

I_{1}, I_{2}, and I_{3} = Respective area moments of inertia for bending in the plane of the frame for the three members (in^{4}, mm^{4}),

E_{1}, E_{2}, and E_{3} = Respective moduli of elasticity (lb/in^{2}, 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),

*l*_{1}, *l*_{2}, *l*_{3} = Member lengths respectively (in, mm),

References:

Roark's Formulas for Stress and Strain, Seventh Edition

**© Copyright 2000 - 2018, by Engineers Edge, LLC www.engineersedge.com All rights reserved
Disclaimer
| Feedback | Advertising
| Contact **

Date/Time: