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

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 any Point.

Calculator for Fixed at One End, Supported at the Other, Load at any Point


Lengths m & n
(Used in many equations)

m = (l + a)(l + b) +al
n = al(l + b)

Open: Lengths m and n Calculator


Loads and Moment at Reaction points as Defined

Open: Loads at Reaction points as Defined Beam 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

Between point of fixture and load

General Stress at any Given Point

Between support and load

Between support and load

Open: Stress Between point of fixture and load and Support Calculator


Stress at Critical Locations/Points

Stress at Critical Locations/Points

Open: Greatest Positive Stress at point of fixture and Negative Stress at Load Calculator

Maximum Stress


Deflection at any Point

Between point of fixture and load

Between point of fixture and load

Between support and load

Between support and load

Open: Deflection at point of fixture and load and Between Support at Load Calculator


Critical Deflections

Critical Deflection Calculator

Open: Deflection at Load Calculator

Deflection at Load Equation


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)
m, n = Some calculated 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, Page 405 or,
  • Machinery's Handbook, 23st Edition, Page 261 or,
  • Machinery's Handbook, 27st Edition, Page 26