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

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.

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,

General Stress at any Given Point

For segment length b

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 Critical Locations/Points

Stress at end nearest to segment of length b,

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

Maximum stress is at end nearest to shorter segment.

and

Stress is zero at

Greatest negative stress, at load

Greatest negative stress, at load

Open:Greatest negative stress at load Calculator


Deflection at any Point

For length a,

Deflection at any Point

For length b

Deflection at any Point

Open: Deflection at any point Length a or b Calculator


Critical Deflections

Deflection at load

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:

maximum deflection is in the longer segment

and

maximum deflection is in the longer segment

 


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