Bending, Deflection and Stress Equations Calculator for
Fixed at One End, Supported at the Other, Load at Center

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 One End, Supported at the Other, Load at Center.


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)


Loads and Moment at Reaction points as Defined

Open: Loads at Reaction points as Defined Beam Calculator


General Stress at any Given Point

Stress between point of fixture and load

Open: Stress Between Point of Fixture and Load Beam Calculator


Between support and load

Open: Stress Between Support and Load Beam Calculator


Stress at Critical Locations/Points

Maximum stress at point of fixture

Open: Stress Maximum at Point of Fixture Load Beam Calculator


Stress is zero at x = (3⁄/1l)l
Greatest negative stress at center

Open: Greatest negative stress at center Beam Calculator


Deflection at any Point

Between point of fixture and load

Open: Deflection between point of fixture and load Calculator


Between support and load

Open: Deflection between support and load Calculator


Critical Deflections

Maximum deflection

v = 0.4474l

or

Open: Maximum Deflection Calculator


Deflection at load

Open: Deflection at load Calculator


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, c & d = 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, Page 405 or,
  • Machinery's Handbook, 23st Edition, Page 261 or,
  • Machinery's Handbook, 27st Edition, Page 26

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