Shear Strain

Q. A square shaped slab of lead with side $50\text{cm}$ and thickness $10.0\text{cm}$ is subjected to a shearing force (on its narrow face) of magnitude $9.0\times {10}^4\text{N}$. The lower edge is riveted to the floor as shown in figure. How much is the upper edge displaced, if the shear modulus of lead is $5.6\times {10}^9\text{Pa}$?

1. $4.8\times {10}^{-4}\text{m}$
2. $3.2\times {10}^{-4}\text{m}$
3. $1.6\times {10}^{-4}\text{m}$
4. $0.8\times {10}^{-4}\text{m}$

Q.

The upper end of a wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through an angle of ${30}^o$. Then angle of shear is

1. 12°

2. 0.12°

3. 1.2°

4. 0.012°

Q. A spring is stretched by applying a load to its free end. The strain produced in the spring is

1. shear
2. longitudinal
3. longitudinal and shear
4. Volumetric

Q.

When a spiral spring is stretched by suspending a load on it, the strain produced is called

1. Shearing

2. Longitudinal

3. Volume

4. Transverse

Q.

An ISLB 350@ 486 N/m beam is laterally supported throughout. The following properties are given for the I - section
$I_x=13158.3\times {10}^{4}m{m}^4,$ shape factor $=1.12,f_y=250MPa,{\gamma }_{mo}=1.1$
Assume the section to be a compact section and a case of low shear. The design bending strength will be kNm.

1. 191.39

Q. An RCC beam of width $250mm$ and effective depth $450mm$ is subjected to a factored shear force of $60kN$. The grade of materials used are $M20$ and $Fe415$. The concrete shear strength is $0.8N/m{m}^2$. The spacing (in mm, correct upto two decimal place) of $8mm$ dia two legged stirrups is ___.

1. 300

Q. Calculate the force needed to punch a 1.46 cm diameter hole in a steel plate 1.27cm thick. The ultimate shear strength of steel plate is 345M N/m2 is

Q. A wire of mass $M$ and length $L$ is hanging from point $A$. Find the increase in its length due to its own weight. The Young's modulus of elasticity of the wire is $Y$ and area of cross-section of the wire is $A$.

1. $\frac{mgL}{2AY}$
2. $\frac{mgL}{AY}$
3. $\frac{mgL}{3AY}$
4. $\frac{2mgL}{AY}$

Q. A tangential force $\left(F\right)$ is applied on the surface of the cuboidal box as shown in figure. Find out the shearing strain.

1. $0.025$
2. $0.05$
3. $0.1$
4. $1$

Q.

A vertical metal cylinder of radius 2 cm and length 2 m is fixed at the lower end and a load of 100 kg is put on it. Find (a) the stress (b) the strain and (c) the compression of the cylinder. Young modulus of the metal = $2\times {10}^{11}N{m}^{-2}$.

Q. A cube of side $1\text{m}$ fixed at the lower face is acted upon by a tangential force $F$ on its upper surface. If shearing strain is ${10}^{-2}$ due to force $F$, find the distance that the upper face is sheared with respect to lower face.

1. ${10}^{-3}$ m
2. ${10}^{-2}$ m
3. ${10}^{-4}$ m
4. ${10}^{-1}$ m

Q. Assuming that shear stress of base of a mountain is equal to force per unit area due to its weight, calcualte the maximum possible height(in $\text{km}$) of a mountain on the earth, if breaking stress of a typical rock is $3\times {10}^8{\text{Nm}}^{-2}$ and specific gravity is $3$.

Q. A RC beam of rectangular cross - section of breadth 250 mm and effective depth 450 mm is subjected to a maximum factored shear force of 150 kN. The grade of concrete is M25 and grade of main steel and stirrups are Fe415 and Fe250 respectively. For the area of main steel provided, the design shear strength ${\tau }_c$as per IS 456: 2000 is $0.56N/m{m}^2$. If the beam is designed for collapse limit state then the spacing of 2 - legged 10 mm vertical stirrups to be provided is mm

Q. A state of plane stress consists of uniaxial compressive stress of magnitude 10 kPa on a vertical surface, along with an unknown shear stress. If the largest stress is 12 kPa tension, the magnitude of unknown shear stress (in kPa, round off to two decimals) is___.

1. 16.2

Q. A bar of cross-section A is subjected two equal and opposite tensile forces at its ends consider a plane section of the bar whose normal makes an angle $\theta$ with the axis of the bar.
What is the shearing stress on this plane?

1. $\left(F/3A\right)\sin 2\theta$.
2. $\left(F/2A\right)\sin 2\theta$.
3. $\left(F/4A\right)\sin 2\theta$.
4. $\left(F/5A\right)\sin 2\theta$.

Q.

The maximum longitudinal pitch in bolted joints, subjected to tensile forces will be mm. [Take thickness of plate = 20 mm]

1. 200

Q. A bar of cross-section A is subjected two equal and opposite tensile forces at its ends consider a plane section of the bar whose normal makes an angle $\theta$ with the axis of the bar.
For what value of $\theta$ is the shearing stress maximum?

1. 45
2. 55
3. 65
4. 775

Q. A wire suspended from one end carries a sphere at its other end. The elongation in the wire reduces from $2mm$ to $1.6mm$ on completely immersing the sphere in water. The density of the material of the sphere is

1. 3200 kg/m${}^3$
2. 800 kg/m${}^3$
3. 1250 kg/m${}^3$
4. 5000 kg/m${}^3$

Q. A long rod of radius 1 cm and length 2 m which is fixed at one end is given a twist of 0.8 radian. The shear strain developed will be :

1. 0.001 radians
2. 0.004 radians
3. 0.002 radians
4. 0.04 radians

Q. A square lead slab of side 50 cm and thinness 10 cm is subject to ashearing force (on its narrow face) of $4\times {10}^{4}N$ as shown. Lower edge is $\eta$ is ${10}^{1}0N/m^2$, then upper edge is displaced by

1. 0.1 mm
2. 0.02 mm
3. 0.04 mm
4. 0.004 mm

Q. A $2m$ long rod of radius $1cm$ which is fixed from one end is given a twist of $0.8$ radian. The shear strain developed will be

1. $0.002$
2. $0.004$
3. $0.008$
4. $0.016$

Q. Assuming that shear stress at the base of a mountain is equal to the force per unit area due to its weight. Calculate the maximum possible height of a mountain on the earth if breaking stress of a typical rock is $3\times {10}^{8}N{m}^{-2}$ and its density is then $3\times {10}^{3}kg{m}^{-3}$.
(Take $g=10m{s}^{-2}$)

1. $4km$
2. $8km$
3. $10km$
4. $16km$

Q. The shearing strain produced in a block of metal subjected to a shearing stress of ${10}^{8}N/m^2$ is
(Modulus of rigidity $\eta =8\times {10}^{10}N/m^2)$

1. $1.1\times {10}^{-3}$
2. $1.5\times {10}^{-3}$
3. $1.25\times {10}^{-3}$
4. $1.6\times {10}^{-3}$

Q. A wire of length $1m$ and radius $4mm$ is clamped at upper end. The lower end is twisted by an angle of 30${}^0$. The angle of shear is

1. ${0.12}^0$
2. ${1.2}^0$
3. ${12}^0$
4. ${0.012}^0$

Q. A slightly tapering wire of length / and radii $r_1$ and $r_2(r_2>r_1)$ subjected to twoequal and opposite stretching force $F$ . If young's modulus of materials of wire is$Y,$ then the elongation in the wire is

1. $\frac{Fl}{\pi Y{r}_1/2}$
2. $\frac{2Fl}{\pi Y{r}_1/2}$
3. $\frac{3Fl}{\pi Y{r}_1/2}$
4. $\frac{2FI}{Y{r}_1{r}_2}$

Q. A block is kept on a smooth inclined plane whose angle of inlination is $\theta$ that moves with a constant acceleration so that the block does not slide relative to the inclined plane. If the inclined plane stops, the normal contact force offered by the plane on the block changes by a factor:

1. $\tan \theta$
2. ${\tan }^2\theta$
3. ${\cos }^2\theta$
4. ${\cot }^2\theta$

Q. Two strips of metal are riveted together at their ends by four rivets, each of diameter $6mm$. Assume that each rivet is to carry one quarter of the load. If the shearing stress on the rivet is not to exceed $6.9\times {10}^{7}Pa$, the maximum tension that can be exerted by the riveted strip is then

1. $2\times {10}^{3}N$
2. $15.6\times {10}^{3}N$
3. $7.8\times {10}^{3}N$.
4. $3.9\times {10}^{3}N$

Q. The first resonance length in a closed organ pipe is $50cm$. Then the second resonance length will be

1. $100cm$
2. $150cm$
3. $50cm$
4. $200cm$

Q. A river water is flowing at $5m{s}^{-1}$. The depth of river water is $10m.$ The shearing stress between horizontal layers of the river water is

1. $0.5\times {10}^{-3}N{m}^{-1}$
2. ${10}^{-3}N{m}^{-1}$
3. $2\times {10}^{-3}N{m}^{-1}$
4. $0.1\times {10}^{-3}N{m}^{-1}$

Q. The end of a wire of length 0.5 m and radius ${10}^{-3}m$ is twisted through 0.80 radian. The shearing strain at the surface of wire will be :

1. $1.6\times {10}^{-3}$
2. $1.6\times {10}^3$
3. $16\times {10}^3$
4. $16\times {10}^6$