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 Both Ends, Load at any location.
Moment and Loads at Supports
M = Wab^{2} / l^{2}
W_{1}=(Wb^{2} / l^{3)})(l + 2a)
Open: Moment and Loads at Supports Calculator
Section Modulus Z
Z = I/z
I = Moment of inertia Cross Section : Units in^{4} (m^{4})
z = Distance neutral axis to extreme fiber: Units in (m)
General Stress at any Given Point
For segment length a,
For segment length b
Open:Stress for Segment a and b Calculator
Stress at Critical Locations/Points
Stress at end nearest to
segment of length a,
Stress at end nearest to segment of length b,
Open:Stress at end nearest a or b Calculator
Maximum stress is at end
nearest to shorter segment.
Stress is zero at
and
Greatest negative stress, at
load
Open:Greatest negative stress at load Calculator
Deflection at any Point
For length a,
For length b
Open: Deflection at any point Length a or b Calculator
Critical Deflections
Deflection at load
Open: Deflection at Load Calculator
If b length is the longer
segment and a is the shorter one.
The maximum deflection is in
the longer segment:
and
Where:
E = 
Modulus of Elasticity 
psi 
(N/mm^{2)} 
I = 
Moment of Inertia 
in^{4} 
(mm^{4)} 
W = 
Load 
lbs 
(N) 
s = 
Stress at the crosssection being evaluated 
Lbs/in^{2} 
(N/mm^{2}) 
y = 
Deflection 
inches 
(mm) 
x = 
Some distance as indicated 
inches 
(mm) 
u = 
Some distance as indicated 
inches 
(mm) 
a, b = 
Some distance as indicated 
inches 
(mm) 
L = 
Some distance as indicated 
inches 
(mm) 
= 
Some distance as indicated 
inches 
(mm) 
Z = 
section modulus of the crosssection of the beam = I/z 
in^{3} 
(mm^{3)} 
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
 Machinery's Handbook, 23st Edition
 Machinery's Handbook, 27st Edition
