A material with identical properties in all directions is known as

Hooke's law is valid up to the

The ratio of lateral strain to linear strain is known as

The variation of shear stress in a circular shaft subjected to torsion is

The variation of shear force due to a uniformly distributed load is by

The maximum bending moment in a simply supported beam carrying a point load at mid span is

In a Mohr's circle, the radius gives the value of the

The shear stress on the principal plane is

In a thin cylinder, the ratio of hoop stress to longitudinal stress is

In a thin cylinder, the hoop stress is given by

What do you understand by stress and strain? Explain the St. Venant's principles with neat and clean diagrams.

A circular steel bar of various cross sections is subjected to a pull of $ 800 \text{ kN} $ as shown in figure below. Determine the extension of the bar.

Explain Hooke's law for isotropic and elastic materials.

A bar of $ 24 \text{ mm} $ diameter and $ 400 \text{ mm} $ length is acted upon by an axial load of $ 38 \text{ kN} $. The elongation of the bar and the change in diameter are measured as $ 0.165 \text{ mm} $ and $ 0.0031 \text{ mm} $ respectively. Determine (i) the Poisson's ratio; (ii) the values of the three moduli.

Two parallel walls, $ 8 \text{ m} $ apart, are to be stayed together by a steel rod of $ 30 \text{ mm} $ diameter with the help of washers and nuts at the ends. The steel rod is passed through the metal plates and is heated. When its temperature is raised to $ 90^{\circ}\text{C} $, the nuts are tightened. Determine the pull in the bar when it is cooled to $ 24^{\circ}\text{C} $. (i) if the ends do not yield. (ii) the total yielding at the ends is $ 2 \text{ mm} $. Take $ E = 205 \text{ GPa} $ and coefficient of thermal expansion of steel $ \alpha_s = 11 \times 10^{-6}/^{\circ}\text{C} $.

When does a shaft undergo torsion? Derive an expression for the maximum torque transmitted by a circular solid shaft in torsion.

Two shafts of the same material and of the same lengths are subjected to the same torque. The first shaft is of a solid circular section and second is of hollow circular section whose internal diameter is $ 2/3 $ of the outside diameter. If the maximum shear stress developed in each shaft is also the same, compare the weights of the shaft.

How many kinds of load a beam can be subjected to? Also explain with neat diagrams, how many kinds of support can be provided to beams.

A $ 10 \text{ m} $ long simply supported beam carries two-point loads of $ 10 \text{ kN} $ and $ 6 \text{ kN} $ at $ 2 \text{ m} $ and $ 9 \text{ m} $ respectively from the left end. It also has a uniformly distributed load of $ 4 \text{ kN/m} $ run for the length between $ 4 \text{ m} $ and $ 7 \text{ m} $ from the left end. Draw shear force and bending moment diagrams.

What is the governing differential equation used for finding the deflection of beams? Using the method of integration, derive an expression for the deflection of a cantilever beam subjected to a concentrated point load at the free end.

A simply supported beam of $ 12 \text{ m} $ span carries a concentrated load of $ 30 \text{ kN} $ at a distance of $ 9\text{ m} $ from the end A as shown in figure below. Determine the deflection at the load point and the slopes at the load point and at the two ends. Take $ E = 205 \text{ GPa} $ and $ I = 2 \times 10^9 \text{ mm}^4 $.

A rectangular bar of cross-sectional area $ 10000 \text{ mm}^2 $ is subjected to an axial load of $ 20 \text{ kN} $. Determine the normal and shear stresses on a section which is inclined at an angle of $ 30^{\circ} $ with normal cross-section of the bar.

A rectangular block is subjected to two perpendicular stresses of $ 10 \text{ MPa} $ tension and $ 10 \text{ MPa} $ compression. Determine the stresses on planes inclined at (i) $ 30^{\circ} $, (ii) $ 45^{\circ} $ and (iii) $ 60^{\circ} $ with the plane of compressive stress using the method of Mohr's circle.

A pipe of $ 100 \text{ mm} $ external diameter and $ 20 \text{ mm} $ thickness carries water at a pressure of $ 20 \text{ MPa} $. Determine the maximum and minimum intensities of hoop stresses in the section of pipe. Also, plot the variation of hoop and radial stresses across the thickness of pipe.

Derive an expression for maximum shear stress of a thin cylinder.

What do you understand by strain energy? Define and derive Castigliano's first theorem.

A tensile load of $ 60 \text{ kN} $ is gradually applied to a circular bar of $ 4 \text{ cm} $ diameter and $ 5 \text{ m} $ long. If the value of $ E = 2.0 \times 10^5 \text{ N/mm}^2 $, determine- (i) stretch in the rod; (ii) stress in the rod; (iii) strain energy absorbed by the rod.

A material with identical properties in all directions is known as

Hooke's law is valid up to the

The ratio of lateral strain to linear strain is known as

The variation of shear stress in a circular shaft subjected to torsion is

The variation of shear force due to a uniformly distributed load is by

The maximum bending moment in a simply supported beam carrying a point load at mid span is

In a Mohr's circle, the radius gives the value of the

The shear stress on the principal plane is

In a thin cylinder, the ratio of hoop stress to longitudinal stress is

In a thin cylinder, the hoop stress is given by

What do you understand by stress and strain? Explain the St. Venant's principles with neat and clean diagrams.

A circular steel bar of various cross sections is subjected to a pull of $ 800 \text{ kN} $ as shown in figure below. Determine the extension of the bar.

Explain Hooke's law for isotropic and elastic materials.

A bar of $ 24 \text{ mm} $ diameter and $ 400 \text{ mm} $ length is acted upon by an axial load of $ 38 \text{ kN} $. The elongation of the bar and the change in diameter are measured as $ 0.165 \text{ mm} $ and $ 0.0031 \text{ mm} $ respectively. Determine (i) the Poisson's ratio; (ii) the values of the three moduli.

Two parallel walls, $ 8 \text{ m} $ apart, are to be stayed together by a steel rod of $ 30 \text{ mm} $ diameter with the help of washers and nuts at the ends. The steel rod is passed through the metal plates and is heated. When its temperature is raised to $ 90^{\circ}\text{C} $, the nuts are tightened. Determine the pull in the bar when it is cooled to $ 24^{\circ}\text{C} $. (i) if the ends do not yield. (ii) the total yielding at the ends is $ 2 \text{ mm} $. Take $ E = 205 \text{ GPa} $ and coefficient of thermal expansion of steel $ \alpha_s = 11 \times 10^{-6}/^{\circ}\text{C} $.

When does a shaft undergo torsion? Derive an expression for the maximum torque transmitted by a circular solid shaft in torsion.

Two shafts of the same material and of the same lengths are subjected to the same torque. The first shaft is of a solid circular section and second is of hollow circular section whose internal diameter is $ 2/3 $ of the outside diameter. If the maximum shear stress developed in each shaft is also the same, compare the weights of the shaft.

How many kinds of load a beam can be subjected to? Also explain with neat diagrams, how many kinds of support can be provided to beams.

A $ 10 \text{ m} $ long simply supported beam carries two-point loads of $ 10 \text{ kN} $ and $ 6 \text{ kN} $ at $ 2 \text{ m} $ and $ 9 \text{ m} $ respectively from the left end. It also has a uniformly distributed load of $ 4 \text{ kN/m} $ run for the length between $ 4 \text{ m} $ and $ 7 \text{ m} $ from the left end. Draw shear force and bending moment diagrams.

What is the governing differential equation used for finding the deflection of beams? Using the method of integration, derive an expression for the deflection of a cantilever beam subjected to a concentrated point load at the free end.

A simply supported beam of $ 12 \text{ m} $ span carries a concentrated load of $ 30 \text{ kN} $ at a distance of $ 9\text{ m} $ from the end A as shown in figure below. Determine the deflection at the load point and the slopes at the load point and at the two ends. Take $ E = 205 \text{ GPa} $ and $ I = 2 \times 10^9 \text{ mm}^4 $.

A rectangular bar of cross-sectional area $ 10000 \text{ mm}^2 $ is subjected to an axial load of $ 20 \text{ kN} $. Determine the normal and shear stresses on a section which is inclined at an angle of $ 30^{\circ} $ with normal cross-section of the bar.

A rectangular block is subjected to two perpendicular stresses of $ 10 \text{ MPa} $ tension and $ 10 \text{ MPa} $ compression. Determine the stresses on planes inclined at (i) $ 30^{\circ} $, (ii) $ 45^{\circ} $ and (iii) $ 60^{\circ} $ with the plane of compressive stress using the method of Mohr's circle.

A pipe of $ 100 \text{ mm} $ external diameter and $ 20 \text{ mm} $ thickness carries water at a pressure of $ 20 \text{ MPa} $. Determine the maximum and minimum intensities of hoop stresses in the section of pipe. Also, plot the variation of hoop and radial stresses across the thickness of pipe.

Derive an expression for maximum shear stress of a thin cylinder.

What do you understand by strain energy? Define and derive Castigliano's first theorem.

A tensile load of $ 60 \text{ kN} $ is gradually applied to a circular bar of $ 4 \text{ cm} $ diameter and $ 5 \text{ m} $ long. If the value of $ E = 2.0 \times 10^5 \text{ N/mm}^2 $, determine- (i) stretch in the rod; (ii) stress in the rod; (iii) strain energy absorbed by the rod.

The percentage elongation and the percentage reduction in area depend upon

The property of a material by which it can be drawn to a smaller section by applying a tensile load is called

A shaft is said to be in pure torsion if

Two shafts in torsion will have equal strength if

Which of the following are statically determinate beams?

In a cantilever carrying a uniformly varying load starting from zero at the free end, the shear force diagram

Which one of the following methods is the best for finding slope and deflection?

Which of the following stresses can be determined using Mohr's circle method?

Hoop strain in a thin shell is

Oil tanks, steam boilers, gas pipes are the examples of

Determine the stress in each section of the bar shown in figure below when subjected to an axial tensile load of $ 20 \text{ kN} $. The central section is $ 30 \text{ mm} $ square cross-section, the other portions are of circular section, their diameters being indicated. What will be the total extension of the bar? For the bar material, $ E = 210 \text{ GN/m}^2 $.

The following data relate to a bar subjected to a tensile test: Diameter of bar $ = 25 \text{ mm} $, Tensile load $ = 50 \text{ kN} $, Gauge length $ = 250 \text{ mm} $, Extension of the bar $ = 0.121 \text{ mm} $ and Change in diameter $ = 0.00357 \text{ mm} $. Calculate the Poisson's ratio and the values of three moduli.

The stresses on two mutually perpendicular planes through a point in a body are $ 30 \text{ MPa} $ and $ 15 \text{ MPa} $ both tensile along with a shear stress of $ 25 \text{ MPa} $. Using both analytical and graphical methods, find-
(a) the magnitude and direction of principal stresses;
(b) the magnitude of the normal and shear stresses on a plane on which the shear stress is maximum.

With the help of suitable assumptions, deduce torsion equation for a solid circular shaft.

A hollow steel shaft transmits $ 200 \text{ kW} $ of power at $ 150 \text{ r.p.m.} $ The total angle of twist in a length of $ 5 \text{ m} $ of the shaft is $ 3^{\circ} $. Find the inner and outer diameters of the shaft if the permissible shear stress is $ 60 \text{ MPa} $. Assume modulus of rigidity as $ 80 \text{ GN/m}^2 $.

The given figure shows an overhanging beam: (a) Sketch the shear force and bending moment diagrams giving the important numerical values. (b) Calculate the maximum bending moment and the point at which it occurs.

A cantilever of length 2 meters carries a uniformly distributed load of $ 2500 \text{ N} $ per metre for a distance of 1.25 meters from the fixed end and a point load of $ 1000 \text{ N} $ at the free end. If the section is rectangular $ 120 \text{ mm} $ side and $ 240 \text{ mm} $ deep, find the deflection at the free end. Take $ E = 10000 \text{ N/mm}^2 $.

A simply supported beam of span L carries a uniformly distributed load W per unit run over the whole span. If now the beam be provided with a prop at the centre of the span so that the prop holds the beam to the level of the end supports, find the reaction of the prop. Draw SF and BM diagrams.

What do you mean by principal planes and principal stresses? Derive the expression for principal stresses for a body subjected to direct and shear stresses.

Two planes AB and BC which are at right angles carry shear stresses of intensity $ 17.5 \text{ N/mm}^2 $ while these planes also carry a tensile stress of $ 70 \text{ N/mm}^2 $ and a compressive stress of $ 35 \text{ N/mm}^2 $ respectively. Determine the principal planes and the principal stresses. Also determine the maximum shear stress and the planes on which it acts.

Calculate the change in dimensions of a thin cylindrical shell due to an internal pressure. Also calculate the change in length and diameter of the cylindrical shell.

A cylindrical shell $ 2 \text{ m} $ long which is closed at the ends has an internal diameter of $ 800 \text{ mm} $ and a wall thickness of $ 10 \text{ mm} $. Calculate the circumferential and longitudinal stresses induced and also change in dimensions of the shell if it is subjected to an internal pressure of $ 1.5 \text{ MN/m}^2 $. Take $ E = 205 \text{ GN/m}^2 $ and $ l/m = 0.3 $.

State and prove Castigliano's first theorem.

A beam simply supported over a span of $ 2 \text{ m} $ carries a uniformly distributed load of $ 15 \text{ kN/m} $ over the entire span. Taking $ EI = 2.25 \text{ MN/m}^2 $ and using Castigliano's theorem, determine the deflection at the centre of beam.

The percentage elongation and the percentage reduction in area depend upon

The property of a material by which it can be drawn to a smaller section by applying a tensile load is called

A shaft is said to be in pure torsion if

Two shafts in torsion will have equal strength if

Which of the following are statically determinate beams?

In a cantilever carrying a uniformly varying load starting from zero at the free end, the shear force diagram

Which one of the following methods is the best for finding slope and deflection?

Which of the following stresses can be determined using Mohr's circle method?

Hoop strain in a thin shell is

Oil tanks, steam boilers, gas pipes are the examples of

Determine the stress in each section of the bar shown in figure below when subjected to an axial tensile load of $ 20 \text{ kN} $. The central section is $ 30 \text{ mm} $ square cross-section, the other portions are of circular section, their diameters being indicated. What will be the total extension of the bar? For the bar material, $ E = 210 \text{ GN/m}^2 $.

The following data relate to a bar subjected to a tensile test: Diameter of bar $ = 25 \text{ mm} $, Tensile load $ = 50 \text{ kN} $, Gauge length $ = 250 \text{ mm} $, Extension of the bar $ = 0.121 \text{ mm} $ and Change in diameter $ = 0.00357 \text{ mm} $. Calculate the Poisson's ratio and the values of three moduli.

The stresses on two mutually perpendicular planes through a point in a body are $ 30 \text{ MPa} $ and $ 15 \text{ MPa} $ both tensile along with a shear stress of $ 25 \text{ MPa} $. Using both analytical and graphical methods, find-
(a) the magnitude and direction of principal stresses;
(b) the magnitude of the normal and shear stresses on a plane on which the shear stress is maximum.

With the help of suitable assumptions, deduce torsion equation for a solid circular shaft.

A hollow steel shaft transmits $ 200 \text{ kW} $ of power at $ 150 \text{ r.p.m.} $ The total angle of twist in a length of $ 5 \text{ m} $ of the shaft is $ 3^{\circ} $. Find the inner and outer diameters of the shaft if the permissible shear stress is $ 60 \text{ MPa} $. Assume modulus of rigidity as $ 80 \text{ GN/m}^2 $.

The given figure shows an overhanging beam: (a) Sketch the shear force and bending moment diagrams giving the important numerical values. (b) Calculate the maximum bending moment and the point at which it occurs.

A cantilever of length 2 meters carries a uniformly distributed load of $ 2500 \text{ N} $ per metre for a distance of 1.25 meters from the fixed end and a point load of $ 1000 \text{ N} $ at the free end. If the section is rectangular $ 120 \text{ mm} $ side and $ 240 \text{ mm} $ deep, find the deflection at the free end. Take $ E = 10000 \text{ N/mm}^2 $.

A simply supported beam of span L carries a uniformly distributed load W per unit run over the whole span. If now the beam be provided with a prop at the centre of the span so that the prop holds the beam to the level of the end supports, find the reaction of the prop. Draw SF and BM diagrams.

What do you mean by principal planes and principal stresses? Derive the expression for principal stresses for a body subjected to direct and shear stresses.

Two planes AB and BC which are at right angles carry shear stresses of intensity $ 17.5 \text{ N/mm}^2 $ while these planes also carry a tensile stress of $ 70 \text{ N/mm}^2 $ and a compressive stress of $ 35 \text{ N/mm}^2 $ respectively. Determine the principal planes and the principal stresses. Also determine the maximum shear stress and the planes on which it acts.

Calculate the change in dimensions of a thin cylindrical shell due to an internal pressure. Also calculate the change in length and diameter of the cylindrical shell.

A cylindrical shell $ 2 \text{ m} $ long which is closed at the ends has an internal diameter of $ 800 \text{ mm} $ and a wall thickness of $ 10 \text{ mm} $. Calculate the circumferential and longitudinal stresses induced and also change in dimensions of the shell if it is subjected to an internal pressure of $ 1.5 \text{ MN/m}^2 $. Take $ E = 205 \text{ GN/m}^2 $ and $ l/m = 0.3 $.

State and prove Castigliano's first theorem.

A beam simply supported over a span of $ 2 \text{ m} $ carries a uniformly distributed load of $ 15 \text{ kN/m} $ over the entire span. Taking $ EI = 2.25 \text{ MN/m}^2 $ and using Castigliano's theorem, determine the deflection at the centre of beam.

The ratio of lateral strain to linear strain is known as

The temperature strain in a bar is ___ proportional to the change in temperature.

Moment of inertia of a semi-circle about its XX-axis is given by

The strength of the beam mainly depends on

A cantilever beam AB of length $ l $ has moment $ M $ applied at free end. The deflection at the free end B is given as

A beam of length $ 6 \text{ m} $ carries a point load $ 120 \text{ kN} $ at its centre. The beam is fixed at both ends. The fixing moment at the ends is

Which of the following are usually considered as thin cylinders?

Thin cylinders are frequently required to operate under pressure up to

In thick cylinders, the radial stress in the wall thickness

The stress due to suddenly applied load is ___ times that of gradually applied load.

A steel bar is $ 900 \text{ mm} $ long, its two ends are $ 40 \text{ mm} $ and $ 30 \text{ mm} $ in diameter and the length of each rod is $ 200 \text{ mm} $. The middle portion of the bar is $ 15 \text{ mm} $ in diameter and $ 500 \text{ mm} $ long. If the bar is subjected to an axial tensile load of $ 15 \text{ kN} $, find its total extension, assuming $ E = 200 \text{ GN/m}^2 $.

The following data relate to a bar subjected to a tensile test: Diameter of bar $ = 30 \text{ mm} $, Tensile load $ = 54 \text{ kN} $, Gauge length $ = 300 \text{ mm} $, Extension of the bar $ = 0.112 \text{ mm} $, Change in diameter $ = 0.00366 \text{ mm} $. Calculate the Poisson's ratio and the values of three moduli.

Two mutually perpendicular planes of an element of material are subjected to direct stresses of $ 10.5 \text{ MN/m}^2 $ (tensile) and $ 3.5 \text{ MN/m}^2 $ (compressive) and shear stress of $ 7 \text{ MN/m}^2 $. Using both analytical and graphical methods, find-
(a) the magnitude and direction of principal stresses;
(b) the magnitude of the normal and shear stresses on a plane on which the shear stress is maximum.

With the help of suitable assumptions, deduce torsion equation for a hollow circular shaft.

A hollow circular shaft $ 20 \text{ mm} $ thick transmits $ 294 \text{ kW} $ at $ 200 \text{ r.p.m.} $ Determine the diameters of the shaft if the shear strain due to torsion is not to exceed $ 8.6 \times 10^{-4} $. Assume modulus of rigidity as $ 80 \text{ GN/m}^2 $.

The following figure shows a loaded beam: (a) Sketch the shear force and bending moment diagrams giving the important numerical values.

(b) Calculate the maximum bending moment and the point at which it occurs.

A cantilever of length $ l $ carries uniformly distributed load of $ W $ per unit run for a distance $ \frac{3l}{4} $ from the fixed end. Find the slope and deflection at the free end.

A cantilever of length $ l $ carries a point load $ W $ at the end. If the moment of inertia of the section increases uniformly from $ I $ at the free end to $ 2I $ at the fixed end, calculate the deflection at the free end.

Calculate the change in dimensions of a thin cylindrical shell due to an internal pressure. Also calculate the change in length and diameter of the cylindrical shell.

A cylindrical shell $ 3 \text{ m} $ long which is closed at the ends has an internal diameter of $ 1 \text{ m} $ and a wall thickness of $ 15 \text{ mm} $. Calculate the circumferential and longitudinal stresses induced and also change in dimensions of the shell if it is subjected to an internal pressure of $ 1.5 \text{ MN/m}^2 $. Take $ E = 200 \text{ GN/m}^2 $ and $ 1/m = 0.3 $.

Discuss and derive Lame's theory for thick shells.

Calculate the thickness of metal necessary for a cylindrical shell of internal diameter $ 160 \text{ mm} $ to withstand a pressure of $ 25 \text{ MN/m}^2 $, if maximum permissible tensile stress is $ 125 \text{ MN/m}^2 $.

The ratio of lateral strain to linear strain is known as

The temperature strain in a bar is ___ proportional to the change in temperature.

Moment of inertia of a semi-circle about its XX-axis is given by

The strength of the beam mainly depends on

A cantilever beam AB of length $ l $ has moment $ M $ applied at free end. The deflection at the free end B is given as

A beam of length $ 6 \text{ m} $ carries a point load $ 120 \text{ kN} $ at its centre. The beam is fixed at both ends. The fixing moment at the ends is

Which of the following are usually considered as thin cylinders?

Thin cylinders are frequently required to operate under pressure up to

In thick cylinders, the radial stress in the wall thickness

The stress due to suddenly applied load is ___ times that of gradually applied load.

A steel bar is $ 900 \text{ mm} $ long, its two ends are $ 40 \text{ mm} $ and $ 30 \text{ mm} $ in diameter and the length of each rod is $ 200 \text{ mm} $. The middle portion of the bar is $ 15 \text{ mm} $ in diameter and $ 500 \text{ mm} $ long. If the bar is subjected to an axial tensile load of $ 15 \text{ kN} $, find its total extension, assuming $ E = 200 \text{ GN/m}^2 $.

The following data relate to a bar subjected to a tensile test: Diameter of bar $ = 30 \text{ mm} $, Tensile load $ = 54 \text{ kN} $, Gauge length $ = 300 \text{ mm} $, Extension of the bar $ = 0.112 \text{ mm} $, Change in diameter $ = 0.00366 \text{ mm} $. Calculate the Poisson's ratio and the values of three moduli.

Two mutually perpendicular planes of an element of material are subjected to direct stresses of $ 10.5 \text{ MN/m}^2 $ (tensile) and $ 3.5 \text{ MN/m}^2 $ (compressive) and shear stress of $ 7 \text{ MN/m}^2 $. Using both analytical and graphical methods, find-
(a) the magnitude and direction of principal stresses;
(b) the magnitude of the normal and shear stresses on a plane on which the shear stress is maximum.

With the help of suitable assumptions, deduce torsion equation for a hollow circular shaft.

A hollow circular shaft $ 20 \text{ mm} $ thick transmits $ 294 \text{ kW} $ at $ 200 \text{ r.p.m.} $ Determine the diameters of the shaft if the shear strain due to torsion is not to exceed $ 8.6 \times 10^{-4} $. Assume modulus of rigidity as $ 80 \text{ GN/m}^2 $.

The following figure shows a loaded beam: (a) Sketch the shear force and bending moment diagrams giving the important numerical values.

(b) Calculate the maximum bending moment and the point at which it occurs.

A cantilever of length $ l $ carries uniformly distributed load of $ W $ per unit run for a distance $ \frac{3l}{4} $ from the fixed end. Find the slope and deflection at the free end.

A cantilever of length $ l $ carries a point load $ W $ at the end. If the moment of inertia of the section increases uniformly from $ I $ at the free end to $ 2I $ at the fixed end, calculate the deflection at the free end.

Calculate the change in dimensions of a thin cylindrical shell due to an internal pressure. Also calculate the change in length and diameter of the cylindrical shell.

A cylindrical shell $ 3 \text{ m} $ long which is closed at the ends has an internal diameter of $ 1 \text{ m} $ and a wall thickness of $ 15 \text{ mm} $. Calculate the circumferential and longitudinal stresses induced and also change in dimensions of the shell if it is subjected to an internal pressure of $ 1.5 \text{ MN/m}^2 $. Take $ E = 200 \text{ GN/m}^2 $ and $ 1/m = 0.3 $.

Discuss and derive Lame's theory for thick shells.

Calculate the thickness of metal necessary for a cylindrical shell of internal diameter $ 160 \text{ mm} $ to withstand a pressure of $ 25 \text{ MN/m}^2 $, if maximum permissible tensile stress is $ 125 \text{ MN/m}^2 $.

A localised compressive stress at the area of contact between two members is known as:

In case of a circular section the section modulus is given as:

For no tension in the section, the eccentricity must not exceed:

The slope and deflection at the section in a loaded beam can be found out by which of the following methods?

A cantilever of length $ l $ is carrying a uniformly distributed load of $ w $ per unit run over the whole span. The deflection at the free end is given as:

A beam of length $ 4 \text{ m} $, fixed at both ends carries a point load $ 120 \text{ kN} $ at the centre. If $ EI $ for the beam is $ 20000 \text{ kNm}^2 $, deflection at the centre of the beam is:

Pressure vessels are made of:

In thick cylinders the variation in the radial as well as circumferential stress across the thickness is obtained with the help of:

The strength of a hollow shaft for the same length, material and weight is ___ a solid shaft:

In case of a solid shaft strain energy in torsion, per unit volume is equal to:

A rod of length "$ l $" tapers uniformly from diameter $ d_1 $ to a diameter $ d_2 $. Its wider end is fixed and lower end is subjected to an axial tensile load $ P $. Calculate the elongation in case of above taper rod.

A bar of steel is $ 60 \text{ mm} \times 60 \text{ mm} $ in section and $ 180 \text{ mm} $ long. It is subjected to a tensile load of $ 300 \text{ kN} $ along the longitudinal axis and tensile loads of $ 750 \text{ kN} $ and $ 600 \text{ kN} $ on the lateral faces. Find the change in the dimensions of the bar and change in the volume. Take $ E = 200 \text{ GN/m}^2 $ and $ 1/m = 0.3 $.

Draw the Mohr's stress circle for the direct stresses of $ 65 \text{ MN/m}^2 $ (tensile) and $ 35 \text{ MN/m}^2 $ (compressive) and estimate the magnitude and direction of the resultant stresses on the planes making angles of $ 20^{\circ} $ and $ 65^{\circ} $ with the plane of the first principal stress. Find also the normal and tangential stresses on these planes.

What is shaft Couplings?

A solid steel shaft is subjected to a torque of $ 45 \text{ kNm} $. If the angle of twist is $ 0.5^{\circ} $ per metre length of the shaft and the shear stress is not allowed to exceed $ 90 \text{ MN/m}^2 $. find: (i) Suitable diameter for the shaft, (ii) Final maximum shear stress and angle of twist and (iii) Maximum shear strain in the shaft, assume $ C = 80 \text{ GN/m}^2 $.

A simple beam with an overhang is supported at points A and B (Figure 1). A uniform load of intensity $ q = 200 \text{ lb/ft} $ acts throughout the length of the beam and a concentrated load $ P = 14 \text{ k} $ at a point $ 9 \text{ ft} $ from the left-hand support. The span length is $ 24 \text{ ft} $ and the length of the overhang is $ 6 \text{ ft} $. Calculate the shear force V and bending moment M at cross section D located $ 15 \text{ ft} $ from the left-hand support.

Assuming suitable example discuss "Moment area method" to find the defection of beam. Why Moment area method is more useful as compared to double integration method.

A cantilever of length $ l $ carrying uniformly distributed load $ w $ per unit run for a distance $ a $ from the fixed end. Calculate deflection at the end of uniformly distributed load and at the end of cantilever.

Define (i) Hoops stresses (ii) Longitudinal stresses and (iii) Maximum shear stress induced in context to thin shells.

A built up cylindrical shell of $ 300 \text{ mm} $ diameter, $ 3 \text{ m} $ long and $ 6 \text{ mm} $ thick is subjected to an internal pressure of $ 2 \text{ MN/m}^2 $. Calculate the change in length, diameter and volume of the cylinder under that pressure if the efficiencies of the longitudinal and circumferential joints are 80% and 50% respectively. Take $ E = 200 \text{ GN/m}^2 $ and $ m = 3.5 $.

Calculate circumferential and radial stress in a thick cylinder assuming internal pressure $ = P_i $ and outer surface of cylinder is exposed to atmospheric conditions.

A thick cylinder of $ 150 \text{ mm} $ outside radius and $ 100 \text{ mm} $ inside radius is subjected to an external pressure of $ 30 \text{ MN/m}^2 $ and the internal pressure of $ 60 \text{ MN/m}^2 $. Calculate the maximum shear stress in the material of the cylinder at the inner radius.

Consider a solid circular shaft of length $ l $ and radius $ R $, subjected to a torque $ T $ producing a twist in the length of the shaft. Calculate strain energy in torsion.

A $ 1 \text{ m} $ long beam rectangular in section $ 30 \text{ mm} $ wide and $ 40 \text{ mm} $ deep is supported on rigid supports at its ends. If it is struck at the centre by a $ 12 \text{ kg} $ mass falling through a height of $ 60 \text{ mm} $ find: (i) The instantaneous stress developed and (ii) The instantaneous strain energy stored in the beam. Take $ E = 200 \text{ GN/m}^2 $.

A localised compressive stress at the area of contact between two members is known as:

In case of a circular section the section modulus is given as:

For no tension in the section, the eccentricity must not exceed:

The slope and deflection at the section in a loaded beam can be found out by which of the following methods?

A cantilever of length $ l $ is carrying a uniformly distributed load of $ w $ per unit run over the whole span. The deflection at the free end is given as:

A beam of length $ 4 \text{ m} $, fixed at both ends carries a point load $ 120 \text{ kN} $ at the centre. If $ EI $ for the beam is $ 20000 \text{ kNm}^2 $, deflection at the centre of the beam is:

Pressure vessels are made of:

In thick cylinders the variation in the radial as well as circumferential stress across the thickness is obtained with the help of:

The strength of a hollow shaft for the same length, material and weight is ___ a solid shaft:

In case of a solid shaft strain energy in torsion, per unit volume is equal to:

A rod of length "$ l $" tapers uniformly from diameter $ d_1 $ to a diameter $ d_2 $. Its wider end is fixed and lower end is subjected to an axial tensile load $ P $. Calculate the elongation in case of above taper rod.

A bar of steel is $ 60 \text{ mm} \times 60 \text{ mm} $ in section and $ 180 \text{ mm} $ long. It is subjected to a tensile load of $ 300 \text{ kN} $ along the longitudinal axis and tensile loads of $ 750 \text{ kN} $ and $ 600 \text{ kN} $ on the lateral faces. Find the change in the dimensions of the bar and change in the volume. Take $ E = 200 \text{ GN/m}^2 $ and $ 1/m = 0.3 $.

Draw the Mohr's stress circle for the direct stresses of $ 65 \text{ MN/m}^2 $ (tensile) and $ 35 \text{ MN/m}^2 $ (compressive) and estimate the magnitude and direction of the resultant stresses on the planes making angles of $ 20^{\circ} $ and $ 65^{\circ} $ with the plane of the first principal stress. Find also the normal and tangential stresses on these planes.

What is shaft Couplings?

A solid steel shaft is subjected to a torque of $ 45 \text{ kNm} $. If the angle of twist is $ 0.5^{\circ} $ per metre length of the shaft and the shear stress is not allowed to exceed $ 90 \text{ MN/m}^2 $. find: (i) Suitable diameter for the shaft, (ii) Final maximum shear stress and angle of twist and (iii) Maximum shear strain in the shaft, assume $ C = 80 \text{ GN/m}^2 $.

A simple beam with an overhang is supported at points A and B (Figure 1). A uniform load of intensity $ q = 200 \text{ lb/ft} $ acts throughout the length of the beam and a concentrated load $ P = 14 \text{ k} $ at a point $ 9 \text{ ft} $ from the left-hand support. The span length is $ 24 \text{ ft} $ and the length of the overhang is $ 6 \text{ ft} $. Calculate the shear force V and bending moment M at cross section D located $ 15 \text{ ft} $ from the left-hand support.

Assuming suitable example discuss "Moment area method" to find the defection of beam. Why Moment area method is more useful as compared to double integration method.

A cantilever of length $ l $ carrying uniformly distributed load $ w $ per unit run for a distance $ a $ from the fixed end. Calculate deflection at the end of uniformly distributed load and at the end of cantilever.

Define (i) Hoops stresses (ii) Longitudinal stresses and (iii) Maximum shear stress induced in context to thin shells.

A built up cylindrical shell of $ 300 \text{ mm} $ diameter, $ 3 \text{ m} $ long and $ 6 \text{ mm} $ thick is subjected to an internal pressure of $ 2 \text{ MN/m}^2 $. Calculate the change in length, diameter and volume of the cylinder under that pressure if the efficiencies of the longitudinal and circumferential joints are 80% and 50% respectively. Take $ E = 200 \text{ GN/m}^2 $ and $ m = 3.5 $.

Calculate circumferential and radial stress in a thick cylinder assuming internal pressure $ = P_i $ and outer surface of cylinder is exposed to atmospheric conditions.

A thick cylinder of $ 150 \text{ mm} $ outside radius and $ 100 \text{ mm} $ inside radius is subjected to an external pressure of $ 30 \text{ MN/m}^2 $ and the internal pressure of $ 60 \text{ MN/m}^2 $. Calculate the maximum shear stress in the material of the cylinder at the inner radius.

Consider a solid circular shaft of length $ l $ and radius $ R $, subjected to a torque $ T $ producing a twist in the length of the shaft. Calculate strain energy in torsion.

A $ 1 \text{ m} $ long beam rectangular in section $ 30 \text{ mm} $ wide and $ 40 \text{ mm} $ deep is supported on rigid supports at its ends. If it is struck at the centre by a $ 12 \text{ kg} $ mass falling through a height of $ 60 \text{ mm} $ find: (i) The instantaneous stress developed and (ii) The instantaneous strain energy stored in the beam. Take $ E = 200 \text{ GN/m}^2 $.