Bending, Deflection and Stress Equations Calculator for Both Ends Overhanging Supports, Load at any Point Between

Beam Deflection and Stress Formula and Calculators

Area Moment of Inertia Equations & Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam with Both Ends Overhanging Supports, Load at any Point Between.

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Section Modulus Z

Z = I/z

I = Moment of inertia Cross Section : Units in⁴ (m⁴)
z = Distance neutral axis to extreme fiber: Units in (m)

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General Stress

Stress at Load:

If cross-section is constant, this is the maximum stress.

Open: Stress at Load Beam Calculator

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General Stress at any Given Point

Between supports:

For area length a,

Open: Stress Between Supports Length a Beam Calculator

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For area of length b,

Open: Stress Between Supports Length b Beam Calculator

Beyond supports s = 0

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Deflection at Critical Locations/Points

Deflection at any Point

Between supports for overhanging end of length c

Open: Deflection overhanging end of length c Beam Calculator

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for overhanging end of length d

Open: Deflection overhanging end of length d Beam Calculator

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Where:

E =	Modulus of Elasticity	psi	(N/mm2)
I =	Moment of Inertia	in4	(mm4)
W =	Load	lbs	(N)
s =	Stress at the cross-section being evaluated	Lbs/in2	(N/mm2)
y =	Deflection	inches	(mm)
x =	Some distance as indicated	inches	(mm)
u =	Some distance as indicated	inches	(mm)
a, b, c & d =	Some distance as indicated	inches	(mm)
L =	Some distance as indicated	inches	(mm)
l =	Some distance as indicated	inches	(mm)
Z =	section modulus of the cross-section of the beam = I/z	in3	(mm3)
z =	distance from neutral axis to extreme fiber (edge)	inches	(mm)

• Please note letter "l" (lower case "L") is different than "I" (Moment of Inertia).
• Deflections apply only to constant cross sections along entire length.

References:

• Any Machinery's Handbook published since 1931 or,
• Machinery's Handbook, 21st Edition, Page 405 or,
• Machinery's Handbook, 23st Edition, Page 261 or,
• Machinery's Handbook, 27st Edition, Page 26