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

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, Load at any location.


Moment and Loads at Supports

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

Open: Moment and Loads at Supports Calculator


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

For segment length a,

For segment length b

Open:Stress for Segment a and b Calculator


Stress at Critical Locations/Points

Stress at end nearest to segment of length a,

Stress at end nearest to segment of length b,

Open:Stress at end nearest a or b Calculator

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

and

Greatest negative stress, at load

Open:Greatest negative stress at load Calculator


Deflection at any Point

For length a,

For length b

Open: Deflection at any point Length a or b Calculator


Critical Deflections

Deflection at load

Open: Deflection at Load Calculator

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

The maximum deflection is in the longer segment:

and

 


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)
= 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 "" (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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