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QUESTION: 1

If the principal stresses at point in a strained body are p_{1} and p_{2} ( p_{1} > p_{2}), then th e resu lta n t stress on a plane carrying the maximum shear stress is equal to

Solution:

Plane of maximum shear is at 45°

QUESTION: 2

If ∈_{1} and ∈_{2} ( ∈_{1} > ∈_{2}) are the m axim um and minimum strains in the neighbourhood of a point in a stressed material of Young’s modulus E and Poisson’s ratio p, then the maximum principal stress will be given by

Solution:

QUESTION: 3

On the element shown below in the figure, the stress in MPa are

The radius of Mohr’s circle V and principal stresses σ_{1}, and σ_{2} are in (MPa) respectively

Solution:

⇒ σ_{1,2} = 70 ± 50

∴ σ_{1 }=_{ }120 MPa

_{and }σ_{2 }= 20 MPa

and, radius of Mohr's circle

QUESTION: 4

The radius of Mohr’s circle gives the value of

Solution:

QUESTION: 5

A body is subjected to two normal strains of magnitude ∈_{x} = 0.003 and ∈_{y} = 0.002. The shearing strain on a plane inclined at 30° with ∈_{x} is

Solution:

Shearing strain

= (∈_{x} - ∈_{y}) sin2θ

= (0.003 - 0.002)sin60°

= √3/2 x 10^{-3}

QUESTION: 6

Which one of the following Mohr’s circles represents the state of pure shear?

Solution:

QUESTION: 7

A bar is subjected to a uniaxial tensile stress ‘σ’. The tangential stress on a plane inclined at θ to the bar would be

Solution:

Normal sress = σ cos^{2} θ

Tangential Stress = σ sin θ cos θ

= σ sin 2θ/2

QUESTION: 8

Which of the following formulae is used to calculate tangential stress, when a member is subjected to stress in mutually perpendicular axis and accompanied by shear stress?

Solution:

QUESTION: 9

Normal stresses of equal magnitude a, but of opposite signs, act at a point of a strained material in perpendicular direction. What is the magnitude of the stress on a plane inclined at 45° to the applied stresses?

Solution:

Here, σ_{x} = σ_{y} = -σ and θ = 45^{°}

∴ σ_{θ} = 0

QUESTION: 10

Two planes xyand yz are passing through a point in a strained material. The normal and shear stresses on xy plane are +80 MPa, -30 MPa respectively and normal and shear stresses on plane yz are +30 MPa and +30 MPa respectively. What is the angle between the planes?

Solution:

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