Beam Deflection and Stress Equations and Calculator Beam Uniform Loading

Beam Deflection and Stress Formula and Calculators

Area Moment of Inertia Equations & Calculators

Stress Equations and Calculator for a Beam Supported One End, Cantilevered at Defined Location and Uniform loading Applied

Figure 1

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Reaction and Shear Equation

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Bending Moments Equation

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Deflection and End Slope Equation

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Where:

E =	Modulus of Elasticity	psi
I =	Area Moment of Inertia	in4
W =	Load, Total	lbf
w =	Unit Load	lbs/in
yx =	Deflection at x ≤ L	inches
yx1 =	Deflection at x1 ≤ a	inches
M1, =	Moment @ formula calc'd distance x	lbs-in
MB, =	Moment @ B	lbs-in
Mx =	Moment @ distance x	lbs-in
Mx1 =	Moment @ distance x1 ≤ a	lbs-in
a, b, c, d, x, L =	Some distance as indicated	inches
RA =	Reaction force at support A	lbf
RB =	Reaction force at support B	lbf
V1 =	Shear Load see Figure 1	lbf
V2 =	Shear Load see Figure 1	lbf
Vx =	Shear Load see Figure 1	lbf
Vx1 =	Shear Load see Figure 1	lbf
θA =	Slope Angle @ x = 0	Rad
θx =	Slope Angle	Rad
θB =	Slope Angle @ x1 = 0	Rad
θC =	Slope Angle @ see equation	Rad
θx1 =	Slope Angle	Rad

• Deflections apply only to constant cross sections along entire length.

References:

• Boeing Design Manual, Rev G. 1994 BDM

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