### Beam Deflection and Stress Equations Calculator for Fixed at Both Ends, Load at any location Beam

Beam Deflection and Stress Formula and Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam Fixed at Both Ends, Load at any location.

Beam Moment and Loads at Supports

M = Wab2 / l2
W1=(Wb2 / l3))(l + 2a)

Beam 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)

General Beam Stress at any Given Point

Beam Stress For segment length a,

Beam Stress For segment length b

Beam Stress at Critical Locations Points

Beam Stress at end nearest to segment of length a,

Beam Stress at end nearest to segment of length b,

Maximum Beam stress is at end nearest to shorter segment.
Beam Stress is zero at

and

Greatest negative Beam stress, at load

Beam Deflection at any Point

For length a,

For length b

Critical Beam Deflections

Beam Deflection at load

If b length is the longer segment and a is the shorter one.

The maximum Beam deflection is in the longer segment:

and

Where:

 E = Beam Modulus of Elasticity psi (N/mm2) I = Beam Moment of Inertia in4 (mm4) W = Beam  Load lbs (N) s = Beam Stress at the cross-section being evaluated Lbs/in2 (N/mm2) y = Beam 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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