Principles of Dairy Machine Design

Module 3. Stress

Lesson 12
SOLVING NUMERICAL

12.1 Problem

A rod of 100m long and of 2mx2m cross section is under pull of 1000N force. If the modulus of elasticity of the material is 2 x 10⁶ N/m², determines the elongation of the rod.

Sol.

Given Length of the rod, l=100m

Area of the rod, A=2x2=4m²

Load P=1000N

Modulus of elasticity E=2x10⁶N/m²

Let ∂ l=elongation of the rod.

Using the relation

12.2 Problem

A brace bar contain ABCD points 1 mt apart from each other of 10m² Area of cross section is subjected to axial force is as shown in fig. Take E=0.8x10⁶ N/m²

Fig.12.1 Brass bar

12.3 Problem

A compound bar is as shown in fig. Calculate the total strain of the composite bar?

Take E=200GPa

=200x10³N/mm²

Fig.12.2 Compound bar

Total elongation δℓ= δℓ₁+ δℓ₂+ δℓ₃ or ∂ ℓ= ∂ ℓ₁+ ∂ ℓ₂+ ∂ ℓ₃