Beam Deflection and Stress Equations Calculator for Beam Supported on Both Ends With Overhanging Supports of equal Length and Uniform Loading

Beam Deflection and Stress Formula and Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam Supported on Both Ends With Overhanging Supports of equal Length and Uniform Loading .

Beam Stress between nearest support point and outer end

Beam Stress between the two supports

Beam Stress at supports

If cross-section is constant, the greater of these is the maximum stress.

If l is greater than 2c, the stress is zero at points on both sides of the center.

If Beam cross-section is constant and if l = 2.828c, the stresses at supports and center are equal and opposite, and are:

Beam Deflection between support point and outer end

Beam Deflection between supports

Beam Deflection at the ends

Deflection at center

If l is between 2c and 2.449c, there are maximum upward deflections at points

on both sides of the center, which are,

Where:

 E = Modulus of Elasticity psi (N/mm2) I = 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) c = 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).
• Beam 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

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