Beam Deflection and Stress Equations Calculator for Beam with Both Ends Overhanging Supports, Load at any Point Between

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam with Both Ends Overhanging Supports, Load at any Point Between.

Beam with Both Ends Overhanging Supports, Load at any Point Between

Beam 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 Beam Stress

Beam Stress at Load:

If cross-section is constant, this is the maximum stress.

General Beam Stress at any Given Point

Between supports:

Beam Stress For area length a,

Beam Stress For area of length b,

Beyond supports s = 0

Beam Deflection at Critical Locations/Points

Beam Deflection at any Point

Beam Deflection Between supports for overhanging end of length c

Beam deflection for overhanging end of length d

Where:

E =	Modulus of Elasticity	psi	(N/mm²)
I =	Moment of Inertia	in⁴	(mm⁴⁾
W =	Load	lbs	(N)
s =	Beam Stress at the cross-section being evaluated	Lbs/in²	(N/mm²)
y =	Beam 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)
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: