ADVANCED STRENGTH OF MATERIALS UNIT :5

UNIT : 5 Advanced topics in bending of stress
1) What are the assumptions made in the analysis of curved bar?
1. Plane section remains plain during bending.
2. The material obeys Hooke’s law.
3. Radial strain is negligible.
4. Each layer is free to expand or contract, independently of the layer above or below it.
2) Define unsymmetrical bending
If the plane of loading or that of bending does not lie in (or parallel to) a plane that contains the principal
centroidal axis of cross section, the bending is called unsymmetrical bending.
3) What are the reasons for unsymmetrical bending?
1. The section is symmetrical but the load line is inclined to both the principal axis.
2. The section itself is unsymmetrical and the load line is along the centroidal axis.
4) What is shear centre or angle of twist?
The shear centre for any transverse section of the beam is the point of intersection of the bending axis
and the plane of the transverse section.
5) Who postulated the theory of curved beam?
Winkler-bach postulated the theory of curved beam.
6) Define Principal moment of inertia
The perpendicular axis about which the product of inertia is zero is called Principal axes and the
moment of inertia with respect to this axis is called Principal moment of inertia.

7) Define Major and Minor Principal moment of inertia
The perpendicular axis about which the product of inertia is maximum is known as Major Principal
moment of inertia.
The perpendicular axis about which the product of inertia is minimum is known as Minor Principal
moment of inertia.
8) What is the shape of distribution of bending stress in a curved beam?
The shape of distribution of bending stress in a curved beam is Hyperbolic.
9) What is the nature of stress in the inside section of a crane hook?
The nature of stress in the inside section of a crane hook is Tensile.
10) Where is the maximum stress in a ring under tension occurring?
The maximum stress in a ring under tension occurs along the line of action of the load.
11) What is the most suitable section for a crane?
The most suitable section for a crane is trapezoidal section.
12) What is pure bending of a beam?
When the loads pass through the bending axis of a beam, then there shall be pure bending.
13) Write the formula for stress using Winkler–bach Formula
σ = M {1+R^2 [ V]
R*A H^2 R+Y
Where,
σ =Bending stress (i.e.σ h)
M= Bending moment with which the bar is subjected.
R=radius of curvature of curved bar.
A=Area of cross section.
H^2=constant for a cross section.
H^2=1 ∫ y^2 dA
A 1+ y
R
14) How will you calculate stress due to unsymmetrical bending?
σ = Mu.u + Mv.v
Iv.v Iu.u
Where,
u=xcos θ + ysin θ
v=ycos θ - xsin θ
15) How will you calculate the distance of neutral axis from centroidal axis?
yo = - (R-H^2)
(R+H^2)
‘-‘ ive shows that the neutral axis is below centroidal axis.
16) How will you calculate the angle of inclination of neutral axis with respect to principal axis?
α = (tan)^-1(Iuu tanθ)
Ivv
17) How will you calculate Resultant stress in a curved bar subjected to direct stress and bending
stress?
σr = σo + σb
Where,
σo =Direct stress =P/A
σb =Bending stress
18) How will you calculate Resultant stress in a Chain link?
σr = σo + σb
Where,
σo =Direct stress =P*sin θ
2A
σb =Bending stress
19) When is product of inertia Ixy zero?
Product of inertia Ixy becomes zero if the section is symmetrical to X-axis (or) Y-axis (or) both the
axis(X&Y axes).