Stress and Deflection Beam Both Ends Overhanging Supports Symmetrically, Uniform Load

Beam Deflection and Stress Formula and Calculators

Area Moment of Inertia Equations & Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam supported Both Ends Overhanging Supports Symmetrically, Uniform Load

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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)


General Stress at any Given Point

Adjacent end stress:

Open: Adjacent End Stress Beam Calculator


Between indicated supports

Open: Between Indicated Supports Beam Calculator


Stress at Critical Locations/Points

Stress at each support:

Open: Stress at Each Support Beam Calculator


Stress at Center of Beam.

Open: Stress at Center of Beam Calculator


Stress at support next to end of length d:

If l is greater than 2c, the stress is zero at points

On both sides of the center

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


Deflection at any Point

Between supports

Open: Deflection Between Supports Calculator


Between each support and adjacent end,

Open: Deflection Between each Support and Adjacent End Calculator


Deflection at Ends

Open: Deflection at Ends Calculator


Where:

E = Modulus of Elasticity psi

(N/mm2)

I = Moment of Inertia in4 (mm4)
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)
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)
c = Distance as indicated inches (mm)
L = Some distance as indicated inches (mm)
= Some distance as indicated inches (mm)
  • Please note letter "" (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

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