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Frame Deflections Concentrated Lateral Displacement Applied Right Vertical Member Equations and Calculator
Frame Deflections with Concentrated Lateral Displacement Applied Right Vertical Member Equations and Calculator.
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General reaction and deformation expressions with right and left ends pinned
Horizontal Deflection at A:
Reaction locations are pinned therefore, the displacements = 0 = δHA
Angular Rotation at A:
Loading Terms LPH and LPM are given below.
Reaction loads and moments VA and VB, and HB can be evaluated from equilibrium equations after calculating HA and MA.
LPh = Δo ( -1 ); Δo can also be an increase in length l3.
LPm = 0
Reaction locations are pinned therefore, the Moments = 0 = MA = MB
Δo = Displacement (in, mm),
θo = Angular Displacement (radians),
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),
Roark's Formulas for Stress and Strain