Module 2 Principal and shear stresses

The state of stress at a point when completely specified enables one to determine the

1. Maximum shearing stress at the point

2. Stress components on any arbitrary plane containing that point

Which of the above is/are correct?

• Only 1

• Only 2

• Both 1 and 2

• Neither 1 not 2

Consider a plane stress case, where σ_x = 3 Pa, σ_y = 1 Pa and τ_xy = 1 Pa. One of the principal directions with respect to x-axis would be

• 0^o

• 21^o

• 22.5^o

• 23^o

In order to have exactly zero tensile stress at one extreme fiber of a solid circular section (dia - D) subjected to combined direct (compressive) and bending stresses, a normal point load is needed to be placed __________.

•      at a radial distance D/3 from the center

•        at a radial distance D/6 from the center

• beyond a distance of 3D/8 measured towards the core from the periphery

•       at a radial distance D/4 from the center

For the state of stress shown in the below figure, normal stress acting on the plane of maximum shear stress is -

•       75 MPa tension

• 25 MPa compression  

•       75 MPa compression

•        25 MPa tension

In generalized three - dimensional state of stress, the number of independent stress components is

• 4

• 6

• 8

• 9

Match the following related to theories of failure

A. Max normal stress theory 1. Vonmises theory

B. Max shear stress theory 2. Haigh’s theory

C. Max strain energy theory 3. Guest and Tresca theory

D. Max distortion energy theory 4. Rankiness theory.

• 1. A – 4, B – 3, C – 2, D -1

• 1. A – 4, B – 3, C – 1, D - 2

• 1. A – 3, B – 4, C – 1, D - 2

• 1. A – 3, B – 4, C – 2, D -1

Which one of the following theories gives satisfactory results for brittle materials ?

• strain enery theorem

• Maximum Principal Stress Theory

• 1. Shear stress energy theory

• 1. Maximum shear stress theory

Consider the following theories of failure:

A. Maximum stress theory

B. Maximum strain theory

C. Maximum shear stress theory

D. Maximum energy or distortion theory

The most suitable for ductile material is

• A & C

• C & D

• A & B

• B & D

An element in a strained body is subjected to only shear stress of intensity 50 MPa tending to rotate the body in a clockwise direction. What is the magnitude of principal stresses?

• 1. ± 50 MPa

• 1. + 50 MPa, -25 MPa

• 1. + 25 MPa, -50 MPa

• 1. ± 25 MPa

Principal stresses at a point in a plane stressed element are σ_x = σ_y = 500 N/mm². Normal stress on the plane inclined at 45° to the x-axis will be

•        Zero

• 500 N/mm²              

•       1000 N/mm²

•      707 N/mm²