Beam Deflection Calculator and Stress Equations for Fixed at Both Ends with Uniform Loading

Beam Deflection and Stress Formula and Calculators

Area Moment of Inertia Equations & Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam Fixed at Both Ends with Uniform Loading.

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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 at any Given Point

Open: Stress at Given Point x Calculator

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Stress at Critical Locations/Points

Maximum Stress (at fixed ends)

The greatest negative stress (at center)

Open: Maximum Stress and Negative Stress Calculator

Stress is zero at: x = 0.7887l and x = 0.2113l

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Deflection at any Point

Open: Deflection at any Point Calculator

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Critical Deflections

Maximum Deflection (Center of Beam)

Open: Deflection Maximum 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 =	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
• Machinery's Handbook, 23st Edition
• Machinery's Handbook, 27st Edition

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