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 Center.
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)
Loads and Moment at Reaction points as Defined
Open: Loads at Reaction points as Defined Beam Calculator
General Stress at any Given Point
Stress between point of fixture and load
Open: Stress Between Point of Fixture and Load Beam Calculator
Between support and load
Open: Stress Between Support and Load Beam Calculator
Stress at Critical Locations/Points
Maximum stress at point
of fixture
Open: Stress Maximum at Point of Fixture Load Beam Calculator
Stress is zero at x = (3⁄/1l)l
Greatest negative stress at
center
Open: Greatest negative stress at
center Beam Calculator
Deflection at any Point
Between point of fixture and load
Open: Deflection between point of fixture and load Calculator
Between support and load
Open: Deflection between support and load Calculator
Critical Deflections
Maximum deflection
v = 0.4474l
or
Open: Maximum Deflection Calculator
Deflection at load
Open: Deflection at load Calculator
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, c & d = 
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, Page 405 or,
 Machinery's Handbook, 23st Edition, Page 261 or,
 Machinery's Handbook, 27st Edition, Page 26
