Beam Deflection and Stress Equations Calculator for Beam Supported on Both Ends Loaded at any Location

Beam Deflection and Stress Formula and Calculators

Area Moment of Inertia Equations & Calculators

Structural Beam Deflection, Stress, Bending Equations and calculator for Beam Supported on Both Ends Loaded at any Location.

Open
Beam Deflection, Stress Beam Supported on Both Ends Calculator

---

Beam Stress between load and "a" load point

Beam Stress between load and "b" load point

---

Beam Stress at load application

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

---

Beam Deflection for location between load and "a" point

Beam Deflection for location between load and "b" point

---

Maximum Beam deflection at load

Let "a" be the length of the shorter segment and "b" of the longer one.
The maximum deflection

	is in the longer segment, at

---

Where:

E =	Modulus of Elasticity	lbs/in2	(N/mm2)
I =	Moment of Inertia	in4	(mm4)
W =	Load	lbs	(N)
s =	Stress at the cross-section being evaluated	lbs/in2	(N/mm2)
y =	Beam Deflection	inches	(mm)
x =	Some distance as indicated	inches	(mm)
a =	Some distance as indicated	inches	(mm)
b =	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:

• Any Machinery's Handbook published since 1931 or,
• Machinery's Handbook, 21st Edition, Page 404 or,
• Machinery's Handbook, 23st Edition, Page 260 or,
• Machinery's Handbook, 27st Edition, Page 261

Related

• Beam supported One End, Pin Opposite End and two Partial Distributed Load Separated.
• Brittle Failure Theories Computing Safety Factors Excel Spreadsheet Calculator
• Equations and Calculator for a Beam supported One End, Pin Opposite End and One Tapered Distributed Load
• Beam Deflection, Shear and Stress Equations and Calculator for a Beam supported One End, Pin Opposite End and Two Tapered Distributed Load
• Flexural Strengthening of Reinforced Concrete Beam with FRP Laminates Spreadsheet Calculator
• Shear and Stress Equations and Calculator for a Beam supported One End, Pin Opposite End and Triangular Distributed Load
• Calculator for a Beam supported One End, Pin Opposite End and Single Moment at End Applied
• Stress Equations and Calculator for a Beam supported One End, Cantilevered at Defined Location and Single Load at End
• Axial Load Capacities for Single Plates Calculator
• Beam Deflection Equations / Calculator with Ends Overhanging Supports and a Two Equal Loads applied at Symmetrical Locations
• Beam Deflection Equations / Calculator with End Overhanging Supports and a Single Load
• Beam Deflection Equations / Calculator Cantilevered Beam with One Load Applied at End