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

Structural Beam Deflection, Stress, Bending Equations and calculator for a Beam Fixed at One End, Supported at the Other, Load at Center.

Beam Deflection and Stress Fixed at One End, Supported at the Other, Load at Center

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)

Beam Loads and Moment at Reaction points as Defined

General Beam Stress at any Given Point

Beam Stress between point of fixture and load

Beam Stress Between support and load

Beam Stress at Critical Locations/Points

Maximum Beam stress at point of fixture

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

Beam Deflection at any Point

Between point of fixture and load

Beam Deflection Between support and load

Critical Beam Deflections

Maximum Beam deflection

v = 0.4474l

Beam Deflection at load

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: