Stress and Deflection Beam Equation and Calculator Both Ends Overhanging Supports Symmetrically, Uniform Load Equation and Calculator

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam supported Both Ends Overhanging Supports Symmetrically, Uniform Load

Beam Stress and Deflection Supported Beam

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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 at any Given Point

Adjacent end stress:

Beam Stress Between indicated supports

Beam Stress at Critical Locations/Points

Stress at each support:

Beam Stress at Center of Beam.

Beam Stress at support next to end of length d:

If l is greater than 2c, the stress is zero at points

Beam Stress On both sides of the center

If cross-section is constant and if l = 2.828c, the stresses at supports and center are equal and opposite, and are:

Beam Stress On both sides of the center

Beam Deflection at any Point

Between supports

Beam Deflection Between each support and adjacent end,

Beam Deflection at Ends

Where:

E =	Modulus of Elasticity	psi	(N/mm²)
I =	Moment of Inertia	in⁴	(mm⁴)
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)
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)
c =	Distance as indicated	inches	(mm)
L =	Some distance as indicated	inches	(mm)
l =	Some distance as indicated	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: