Principles of Dairy Machine Design

Module 5. Properties of material, failures and factor of safety

Lesson 25
SOLVING NUMERICAL

The load on a bolt consists of an axial pull of 20 KN together with a transverse Shear force of 10 KN. Find the diameter of bolt required according to

• Maximum principal stress theory.

• Maximum distortion energy theory.

• Maximum shear stress theory.

• Maximum strain energy theory; and

• Maximum principal strain theory.

 

Take Permissible Tensile stress at elastics limit=100Mpa and Poisson’s ratio=0.3

Nomenclature

Load=P

б_{t1 =} normal tensile stress in x direction

б_t2 = normal tensile stress in y direction

б_1, б₂= Principal stresses

Shear stress= ז

б_t(el)= Permissible Tensile stress at elastics limit

Sol.

Given load=P_tensile =20KN

P_shear=10KN

(stress(sigma symbol))_{tensile(elongation)}=100Mpa=100N/MM²

µ=1/m=0.3

Let d=diameter of the bolt in mm

Therefore Cross sectional area of the bolt

A = (Π / 4) x d²=0.785*d² mm²

We know that axial tensile stress

б_t1 = (P_t1 / A) = (20 / 0.785d²) = (25.47 / d²) kN / mm²

And transverse shear stress

Shear stress(ז) = ( Ps/ A) = (10 / 0.785d² ) = ( 12.73/ d²) kN/mm²

1). According to maximum principal stress theory.

We know that maximum principal stress,

According to maximum principal stress theory

б_{t1 =} б_t(el)

(30365 / d²) = 100

d² = ( 30365/ 100) = 303.65

= 17.42mm

^{2) According to maximum shear stress theory}

^{We know that maximum shear stress}

^{According to maximum shear stress theory}