Flexure Equation OR Bending Equation

Flexure Equation OR Bending Equation

M/I= 𝜎/𝑦= 𝐸/𝑅

M → Moment of Resistance or max. B.M.

𝜎 → Bending stress induced due to applied B.M.

E → Young’s modulus of Elasticity

R → Radius of Curvature

Bending moment = Lesser

Curvature = Lesser

Radius of curvature= Greater

 B.M. = Greater

Curvature = Greater

Radius of curvature= Lesser

 Curvature = 1/𝑅

1) If B.M. is increases, its curvature increases. As a result, Radius of curvature will decrease.

2) If B.M. decreases, its curvature decreases/ As a result, Radius of Curvature will 

increases.

→ It is the distance from Neutral Axis (NA) to Extreme Fiber.

M = σI/ymax

𝐼 = It is moment of inertia of whole section about Neutral Axis.

 Unit → mm4

Section Modulus (Z)

Z = 𝐈/𝐲

 ∴ unit → mm3

It is a ratio of moment of inertia of whole section about neutral axis to distance from 

neutral axis to extreme fiber.

Z = moment of Inertia of whole Section about N.A / Distance from N.A to extreme Fibre 

M = 𝜎 Z

NOTE:-

1) As the section modulus increases, strength increases. As a result, moment of 

Resistance will increase.

2) While comparing the strength of two sections always compare their section modulus (Z).