Two solid circular bars are as shown in figure 1. Determine force P required for equilibrium. Also find stress in each bar and total change in length of the assembly.

A compound bar is constructed from three bars 50 mm wide and 12mm thick fastened together. Middle bar is copper and outer two bars are of steel. The copper bar has an E = 100 GPa, while the steel bars have E = 200 GPa. Determine the stresses produced in the copper and steel if the bars are originally fastened at 18°C and the temperature of the entire assembly is subsequently raised to 50°C. Coefficient of thermal expansion for copper and steel are 18 × 10–6 per °C and 12 × 10–6 per°C respectively.

A copper rod with a diameter of 40 mm is firmly enclosed by a cast iron tube with an external diameter of 80 mm. The ends of these components are rigidly connected. When subjected to a compressive force of 30 kN, what will be the load borne by each of them? Additionally, calculate the extent to which the compound bar will contract if its length is 2 meters.

A solid steel rod of 40 mm diameter and 4m length is subjected to tensile load of 40 kN. Determine its elongation. If this rod is bored centrally with diameter of 20mm till 3.6m from one side, find increase in elongation. Take modulus of elasticity of steel as 2 × 105 N/mm2.

Plot Shear force and Bending moment diagram for the overhanging beam loaded and supported as shown in Figure 2

Plot Shear force and Bending moment diagram for the cantilever beam loaded and supported as shown in Figure 3

Plot Shear force and Bending moment diagram for the simply supported beam loaded and supported as shown in Figure 4

Fig 5 shows the shear force diagram. Plot loading diagram and bending moment diagram from this shear force diagram.

A steel bar of 20mm diameter is loaded as shown in figure 1. Determine the stresses in each part and the total elongation. Take E = 210 GPa.

A brass rod 2m long is fixed at both its ends. If the thermal stress is not to exceed 76.5 MPa, calculate the temperature through which the rod should be heated. Take the value of alpha as 17 × 10–6/K and E = 90 GPa.

A metal rod 20 mm diameter and 2 m long is subjected to a tensile force of 60 kN, it showed and elongation of 2 mm and reduction of diameter by 0.006 mm. Calculate the Poisson’s ratio and three moduli of elasticity.

A steel rod 500mm long and 20mm 10mm in cross-section is subjected to axial pull of 300 kN. If modulus of elasticity is 2 × 105 N/mm2. Calculate the elongation of the rod. Also calculate strain induced in the bar.

Draw Shear force and Bending moment diagram for the simply supported beam loaded and supported as shown in Figure 2.

Draw Shear force and Bending moment diagram for the Cantilever beam loaded and supported as shown in Figure 3.

Draw Shear force and Bending moment diagram for the simply supported beam loaded and supported as shown in Figure 4.

Draw Shear force and Bending moment diagram for the simply supported beam loaded and supported as shown in Figure 5.

A square bar ABCD of uniform cross section 30 × 30 mm dimension is subjected to loads as shown in Figure 1. Find the total elongation of the bar and the maximum stress in the bar. If E = 200 GPa. Length of members AB = 500 mm, BC = 1100 mm, CD = 900 mm respectively.

A reinforced cement concrete short column 700 mm × 600 mm has eight steel bars of 25 mm diameter as reinforcement. Find the stresses in steel and concrete and the elastic shortening of the column if Es = 210,000 N/mm2 for steel and Ec = 10,000 N/mm2 for concrete. Load on column is 3000 kN having length of column is 3 m.

The length of an aluminium bar 20 mm diameter and 500 mm long increases to 500.22 mm when subjected to a tensile force of 3 kN. Find the stress, strain in the bar and the value of E for aluminium.

A concrete column of size 400 mm × 400 mm is reinforced with six bars of 16 mm diameter is subjected to rise in temperature by 50°C. Determine the stresses developed in steel and concrete by assuming Ec = 13 GPa, Es = 200 GPa and c = 5 × 10–6/°C, s = 12 × 10–6/°C.

Draw the Shear force diagram and Bending moment diagram for a beam ABCD as shown in figure 2.

Draw the Shear force diagram (SFD) and Bending moment diagram (BMD) for a beam ABCD as shown in figure 3.

Draw bending moment diagram and loading diagram from given shear force diagram as shown in figure 4.

Draw the shear force and bending moment diagram of cantilever beam as shown in figure 5.

A steel bar is subjected to forces as shown in the figure below. Determine total elongation of the bar. Take E = 210 GPa.

A steel bar of 20 mm diameter and 1 m long is heated through 40°C with its ends clamped before heating. Calculate magnitude and nature of the stress developed in the bar. If the clamps do not yield. The coefficient of thermal expansion is α = 12 × 10–5/°C and E = 210 GPa.

A steel wire of length 500 mm is subjected to an axial pull of 25 kN. Find minimum diameter of the wire so that the stress does not exceet 190 MPa. Also determine the modulus of Elasticity of wire, do if elongation is 0.5 mm.

A RCC column 500 mm × 500 mm is reinforced with 4 bars of 25 mm diameter. Determine stresses induced in steel and concrete if the column is subjected to an axial load of 600 kN. Ratio of Esteel to Econcrete is 13.

Draw Shear Force Diagram (SFD) and Bending Moment Diagram (BMD).

Draw SFD and BMD for the cantilever beam shown below.

Draw SFD and BMD of the simply supported beam.

SFD of the beam is given below. Draw loading diagram and BMD.

A cantilever beam of span 1.5m is carrying uniformly distributed load of 50kN/m on entire span. The beam is rectangular having 230mm width and 450 mm depth. Determine maximum bending stress and draw Bending stress Distribution diagram.

A beam of ‘T’ section having flange of 800 mm × 50 mm and web of 600 mm × 30mm, is subjected to load, due to which shear force of 100kN is induced in the beam. Draw shear stress Distribution diagram.

A simply supported beam of rectangular cross section is carrying two point loads of 60 kN, each at 2m from each support as shown. The cross section of the beam is shown below. Draw Bending stress Distribution diagram.

Draw shear stress Distribution diagram for the beam having maximum shear force 150kN. The beam is symmetric ‘I’ section having- flanges : 600 mm × 40 mm web : 800 mm × 40 mm

A solid circular shaft is used to transmit 50 kW at 220 rpm. The maximum permissible shear stress is 110 N/mm2 and the angle of twist is not to exceed 1º in the length of 2m. Calculate the diameter of the shaft for safe transmission of the power.

The principal stresses at a point across two mutually perpendicular planes are 110 N/mm2 and 85 N/mm2, both are tensile, Determine the normal, tangential and resultant stress on a plane 30º with major principal plane.

A hollow circular shaft of 250 mm exrernal diameter and thickness 20 mm is rotating at 150 rpm. The angle of twist in 4m length was found to be 0.8º. Calculate the power transmitted by the shaft and the maximum shear stress induced. G = 80 Gpa.

Direct stresses of 200 N/mm2 tensile & 100 N/mm2 compressive are acting on two perpendicular planes at a point in a body. These stresses are accompanied by shear stresses on the planes. The major principal stress is 250 N/mm2 Determine the magnitude of shear stresses on the planes also calculate maximum shear stress at the point.

State the assumptions made in Euler’s theory and its limitations.

Determine the crippling load given by Rankine’s formula for a tubular strut 3.5m long having outer diameter 50mm and inner diameter 40 mm. Assume both ends pinjointed. Consider fy = 315 mpa and α = 1/7000

A rectangular column of 500 mm × 300 mm is carrying a compressive load of 150 kN acting at an eccentricity of 40 mm in a plane bisecting 300 mm side. Determine maximum and minimum stresses.

Explain core of a section. Determine core of section for a rectangular column of size B×D.

Determine crippling load by Euler’s formula for a column 5m long with one end fixed and other end hinged. The diameter of the solid column is 60 mm E = 210 Gpa.

A hollw tabular steel strut is 3m long and having outer diameter 60mm and inner diameter 50 mm. Both end of the column are hinged. Consider yield stress as 315 N/mm2 and Rankines constant as 1/7500 modulus of elasticity is 205 Gpa. Determine crippling load by using Rankine’s formula.

A cantilever beam of span ‘L’ is carrying uniformly distributed load of ‘W’ kN/m on entire span of the beam. Determine maximum slope and deflection in the beam. Use strain Energy method or MaCaulay’s method.

Determine maximum slope and central deflection for a simply supported beam, shown in the figure below.

Determine slope and deflection for a cantilever beam at its free end. The span of the beam is 1m and it is carrying a uniformly distributed load of 30kN/m on entire span, along with a point load of 60 kN at its free end. Use MaCaulay’s method.

Determine horizontal displacement at joint ‘C’ of th truss. The cross sectional area of each member is 250 mm2 E = 200 Gpa

A simply supported beam of rectangular cross section, 350mm wide and 700mm deep is subjected to uniformly distributed load of 120kN/m on entire span of 3m. Determine maximum bending stress and draw Bending stress Distribution diagram.

A ‘T’ beam is having flange 1000mm×100mm and web 800mm × 80mm. The maximum shear force induced in the beam due to applied load is 400 KN. Draw shear strees distribution diagram for the beam.

A cantilever beam of span 1.2m is loaded with a point load of 70KN at its free end. The beam is rectangular in cross section having width 230mm and depth 500mm. Determine maximum bending stress & draw bending stress distribution diagram.

A symmetric ‘I’ section having flanges - 500mm × 25mm web - 800mm × 20mm. Maximum shear force induced in the beam due to applied loading is 300KN. Draw shear stress distribution diagram.

A hollow circular shaft has an external diameter of 120mm and an internal diameter of 100mm. The maximum permissible shear stress is 80 MPa and the twist is not to exceed 3º in length of 3m. The shaft is rotating at 2RPS if the shear modulus of the material is 80 GPa, find the safe power that can be transmitted.

At a point in a material the stress on two mutually perpendicular plane are 140N/mm2 and 70 N/mm2, both tensile. Determine normal, tangential and resultant stress at a plane 20º to the major principal plane.

Find maximum torque that can be applied to a shaft of 100mm diameter. The permissible angle of twist is 1.2º in a length of 3m and permissible shear stress is 70 MPa. G = 80 GPa

An element is subjected to a tensile stress of 120 MPa and a shear strees of 60 MPa tending to rotate the element in an anticlockwise direction. Determine the magnitude of normal and shear stress on a section inclined at 35º with the tensile stress.

A hollow circular column with two ends hinged carrying 10kN axial load. If the outer diameter of the column is 60mm. The column is 6m long. Determine the inner diameter of the column. Factor of safety 2 against buckling. E = 80 GPa.

Determine the crippling load for a hollow rectangular cast iron column of outer dimensions 300mm × 200mm. Thickness of the column is 30mm. The length of the column is 5m having one end fixed and other hinged. E= 160 GPa.

A rectangular column 600mm × 400mm is subjected to compressive load of 200kN acting at an eccentricity of 50mm in a plane bisecting 400mm side. Determine maximum and minimum stresses.

A steel rod 5m long and 100mm diameter is acting as column with one end fixed and other free. Find crippling load by Euler’s formula consider E = 210 GPa

A hollow column, 4m long is fixed at both ends. The external diameter of the column is 350mm and thickness is 25mm. Determine Rankine’s crippling load. taking fc = 550 N/mm2 and 1/1700

Determine the core of section for a circular section of diameter ‘D’.

Determine maximum slope and central deflection for a simply supported beam as shown below. Use Macaulay’s method.

Determine the vertical displacement at joint C by using unit load method Area of the each member of the truss is 400mm2. E = 210 GPa

A cantilever beam of span ‘L’ is subjected to uniformly distributed load of ‘w’ kN/m on entire span. Determine slope and deflection at the free end of the beam, using Macaulay’s method.

Determine horizontal displacement at joint ‘C’. Area of each member of the truss is 450mm2. E = 200 GPa.

A T-section with flange 200mm×50mm and web 200mm×50 mm is subjected to a vertical shear force of 200 kN. Calculate shear stress at the junction of the flange and web and shear stress at the junction of the flange and web and shear stress at the neutral axis. Sketch the shear stress diagram.

A symmetric I section is 150 wide and 200 deep. The flange thickness and web thickness is 10 mm. This section is used for cantilever beam having span of 3 m and subjected to uniformly distributed load. Find the maximum u.d.l. that can be supported if E=200 GPa and maximum allowable stress is 180 MPa.

A T section 100mm×130mm×20mm is subjected to a shear force of 100kN. Draw the shear stress distribution and find the maximum shear stress.

Two Wooden Planks 150mm×50mm each are connected to form a T section of a beam. A moment of 6.4kN-m is applied around the horizontal neutral axis. Find the bending stresses at both the extreme fibers of cross-section (Fig.1)

A bar of steel is 80mm in diameter and 550mm long. A tensile load of 100kN is found to stretch the bar by 0.25 mm. The same bar when subjected to a torque of 1.4kN.m is found to twist through 3º. Find the value of four elastic constant.

A block 120mm×80 mm ×8mm thick is subjected to uniformly distributed stress field as shown in Fig.2 Compute the normal stress and shear stress development along the plane BD. Also find out the maximum shear stress and corresponding plane.

A metal bar 15mm diameter subjected to pull of 40kN elongated by 0.5 mm over a gauge length of 500 mm. In a torsion test on the same material, maximum shear stress of 45 MPa was measured on a bar of 50 mm diameter and angle of twist over a length of 300 mm was measured 0.4º. Determine Poisson’s ratio for the material .

The principal tensile stresses at a point are 100 N/mm2 and 60 N/mm2. Find normal tangential and resultant stress on a plane at 30º with major principal plane. What is angle of obliquity? Show by sketch how normal stress and tangential stress act.

A 4m length of a tube has a buckling load of 2kN when used as a column hinged at both ends. Calculate buckling load for 4.5 m length of the same tube when used as column if: i) Both ends are fixed ii) One end fixed and other is hinged

A short masonry pillar 600 mm×600 mm in section. The pillar carries an eccentric load of 1000kN acting at an eccentricity of 80 mm from the longitudinal axis as shown in Fig. Find the maximum and minimum stresses on the section.

A steel rod 5 m long and of 40 mm diameter is used as a column with one end fixed and other end free. Determine the crippling load by Euler’s formula. Take E=200 GPa.

A column support load of 400 kN is shown in Fig. Find the stresses at the correct of the column at its base.

A simply supported beam of 3 m span carries two point load of 120kN at a distance 0.6m and 2m form the left support. If for the beam I=16×108 mm4 and E=2×105 N/mm2, calculate the deflection under loads using Macaulay’s Method.

A rectangular beam 80mm wide and 100mm is 4.5m long and subjected to two point loads 20kN and 15kN at 2m and 3.5m from left supports. Determine strain energy stored in the beam. Take E=200 GPa.

A beam of uniform section, 10m long is simply supported at the ends. It carries point loads of 150kN and 65kN at distance of 2.5m and 5.5m respectively from the left end. Calculate: i) Deflection under each load ii) Maximum Deflection Take E=200 kN/m2 and I=118×10-4 m4

A simply supported beam 4m span with EI constant throughout is subjected to a point load of 24kN at 3 m from left hand support. Find the strain energy of the beam is bending.

A simply supported beam of rectangular section 230 mm wide and 450 mm deep is subjected to uniformly distributed load of 60 kN/m on entire span of 4m. Determine maximum bending stress and draw Bending stress Distribution diagram.

A symmetric ‘I’ section having flanges each of 150 mm × 20 mm and web of 200 mm × 20mm is subjected to a shear force of 100 kN. Draw shear stress Distribution diagram of the beam.

A cantilever beam of span 1m is subjected to two point loads, 100kN at the free end and 50kN at the centre of the beam. The beam is rectangular in section having width of 300 mm and depth 600mm. Determine maximum bending stress and draw Bending stress Distribution diagram.

A beam of ‘T’ section having flange of 300 mm × 50mm and web of 400mm × 50mm, is subjected to maximum shear force of 200 KN. Draw Shear stress Distribution diagram.

A solid aluminium shaft of 80mm diameter is to be replaced by a hollow steel shaft of 80mm outer diameter. The two shafts have same angle of twist per unit torque over the total length. If the shear modulus of steel is three times the shear modulus of aluminium. Find the inner diameter of the shaft.

The principal tensile stresses at a point are 85N/mm2 and 55N/mm2. Find the normal, tangential and resultant stress on a plane at 25º with major principal plane. Also find the angle of obliquity.

Find maximum torque that can be safely applied to a shaft of 75mm diameter. The permissible angle of twist is 1º in a length of 4m and permissible shear stress is 40 Mpa. Take G = 80 Gpa.

Direct stresses of 150 N/mm2 and 80 N/mm2, both tensile exists on two perpendicular planes at a point in a body. Shear stress is also acting along with these direct stresses. If the greatest principal stress at the point is 200 N/mm2, determine the magnitude of shear stress on the two planes. Also find the maximum shear stress at the point.

A steel column of 4m long and of 100mm diameter is fixed at one end and free at other end. Determine the crippling load by Euler’s formula. Take E = 200 GPa.

Determine the safe load, an angle strut 75mm × 75 mm × 10mm can carry. The length of the strut is 2m and it is fixed at one end and hinged at the other. Consider factory of safety as 1.5. Minimum radlics of gyration 12.5mm and 6c = 400mpa (crosting 8 trem) a = 1 / 7500. Use Rankine’s formula.

Determine core section for a hollow rectangular column of external size B × D and internal size b × d respectively.

State assumptions and limitations of Euler’s theory.

Determine ratio of Crippling load given by Euler’s and Rankine’s formula for a circular column of 60mm diameter and 2.5m long. Take yield stress as 310 MPa. Rankines constant = 1/7500 and E = 210 GPa.

A rectangular column 300mm × 250mm is subjected to compressive load of 160 kN acting at an eccetricity of 45 mm in a plane bisecting 250 mm side. Determine maximum and minimum stresses.

Determine slope and deflection for a simply supported beam loaded as shown below. Use Macaulay’s method.

Determine the vertical displacement at joint ‘C’ by using unit load method. Area of each member is 500 mm2. E = 210 Gpa.

Determine maximum slope and deflection for a simply supported beam shown in figure below. Use Macaulay’s method.

Determine vertical displacement at joint ‘C’ using unit Load method. Area of each member is 600 mm2 E = 200 GPa.

A cast iron beam has an I-section with top flange 80 mm × 40 mm, web 120 mm × 20 mm and bottom flange 160 mm × 40 mm. If the tensile stress is not to exceed 30 N/mm2 and compressive stress 90 N/mm2, what is the maximum uniformly distributed load the beam can carry over a simply supported beam span 6 m, if the larger flange is in tension.

The unsymmetrical I-section has top flange 80 mm × 20 mm, web 200 mm × 20 mm and bottom flange 160 mm × 40 mm is subjected to shear force of 40kN. Draw shear stress variation diagram across the depth.

A simply supported beam is having 3.5 m long span. Find the maximum udl it can carry. Its allowable compressive and tensile stress are 55 Mpa and 30 Mpa respectively. Draw a diagram showing the variation of stress over mid span section of the beam.

A steel beam of I section, 200 mm deep and 160 mm wide has 16 mm thick flange and 10 mm thick web. The beam is subjected to a shear force of 200 kN. Determine the stress distribution over the beam section if’the web of the beam is kept horizontal.

Calculate the maximum intensity of shear stress induced and the angle of twist produced in degrees in solid shaft of 100mm diameter, 10 m long, transmitting 112.5 kW at 150 rpm. Take G 82 kN/mm2.

The stresses at point in a component are 150 Mpa and 50 Mpa both tensile. Find the intensities of normal, shear and resultant stresses on a plane inclined at an angle of 55º with the axis of major tensile stress. Also find the magnitude of the maximum shear stress in the component.

A solid shaft is subjected to a torque of 1.6 kN-m. find the necessary diameter of the shaft, if the allowable shear stress is 60 Mpa. The allowable twist is 1º for every 20 diameter length of the shaft. Take C=80 Gpa.

At a point in a strained material there is tensile stress of 80 N/mm2 on a horizontal plane and compressive stress at 40 N/mm2 on a vertical plane. There is also a shear stress of 48 N/mm2 on each of these planes. Determine the planes of maximum shear stress at the point. Determine also the resultant stress on the planes of maximum shear stress.

Determine the buckling load for a strut of tee section, the flange width being 100 mm. overall depth 80 mm and both flange and web 10 mm thick. The strut is 3 m long and is hinged at both ends. Take E = 200 GNm2.

A alloy hollow circular column of 200 mm external and 160 mm internal diameter is 5 m long and fixed at both ends. It is subjected to a load of 120 kN at an eccentricity of 20 mm from the axis. Determine the maximum stress induced in the column section. Take E = 120 Gpa.

Find the Euler’s crippling load for a hallow cylindrical steel column of 38 mm external diameter and 2.5 mm thick. Take length of the column as 2.3m and hinged at its both ends. Take E = 205 Gpa. Also determine crippling load by Rankine’s formula using yield stress 335 Mpa and constant 1/7500.

A steel tube of external diameter 109 mm and internal diameter 100 mm is used as a column of length 5 m with both ends hinged. How much axial load can it carry with a factor of safety of 1.75? In case the same load acts with eccentricity of 12 mm, determine the maximum horizontal deflection and the stress in the column. Take E =2 × 105 N/mm2.

A simply supported beam of 6 m span is subjected to a concentrated load of 18 kN at 4 m from the left support. Calculate : i) the position and value ii) slope at mid span iii) deflection at the load point Give E = 200 Gpa, I = 15 × 106 mm4 use Macaulay’s method

Determine the vertical deflection using strain energy method of point C in the frame shown in figure 2. Given E = 200 kN/mm2 and I = 30 × 106 mm4.

A cantilever of beam AB of length L and fixed at end A carries UDL of intensity l0kN/m over the entire span 6m and point load at free end 40 kN. Determine Slope at center and deflection at free end B of beam. Use Castingliano’s theorem.

Determine the horizontal displacement of the joint C of the pin jointed frame as shown in figure 3. The cross section are of AB is 500 mm2 and AC and BC is 750 mm2. Assume E = 200 kN/mm2.

A symmetric I section is having two flanges, each of 300 mm × 20 mm and vertical web of 20 mm thickness and 160 mm depth. The beam is subjected to shear force 200 kN. Draw Shear Force Distribution diagram.

A rectangular simply supported beam of 5m span is subjected to a central point load of 100 kN. The given beam is 300 mm wide and 500 mm deep. Determine maximum bending stress induced in the section. Draw Bending Stress Distribution diagram.

A ‘T’ beam, subjected to shear force of 200 kN. The flange is 200 mm × 30 mm and the web is 30 mm thick and 180 mm deep. Draw shear stress distribution diagram.

A symmetric I section of flanges 120 mm × 20 mm and web of thickness 20 mm and 100 mm depth, carrying uniformly distributed load of magnitude 80 kN/m over 4 m span. Calculate the maximum bending compressive stress.

A solid circular shaft of diameter 90 mm rotates at 130 rpm. The twist is observed as 3º over 6 m span. Determine power transmitted. Take G = 80 GPa.

Determine normal, tangential and resultant stresses on a plane at 25º with major principal plane. The principal stresses of 120 MPa tensile on major principal plane and 50 MPa compressive on minor principal plane are acting at a point on the member.

A solid circular shaft transmits 220 kW at 160 rpm. The maximum allowable shear stress is 60 MPa and angle of twist permitted is 2º in 3m length. Design suitable shaft. Take G = 78 GPa.

A circular bar of diameter 80 mm diameter is subjected to axial compression force of 200 kN. Determine shear stress on a plane, on which the normal stress is 100 MPa.

Compare the crippling loads given by Euler’s and Rankine’s formulae for a steel strut 2.5 m long having outer & inner diameter as 40 mm and 30 mm respectively loaded through pin jointed at the ends. Take yield stress as 320 N/mm2 the Rankine’s constant 1/7500, E = 2 × 105 MPa.

Explain ‘Core of the Section’ and obtain a core section for a hollow circular column of external and internal diameter ‘D’ and ‘d’ respectively.

A steel rod 6m long and 30 mm diameter is used as a column. One end is fixed and other is free. Determine the crippling load by Euler’s formula. Take E = 200 GPa.

A rectangular column of 240 mm × 150 mm is subjected to a vertical load of 110 kN, acting at an eccentricity of 60 mm in a plane bisecting 150 mm side. Determine the maximum and minimum stresses.

The beam is supported and loaded as shown in figure. Determine the position and value of Maximum deflection EI = 1.4 × 1011 kN-mm2. Use Macauly’s method.

Determine the vertical and horizontal deflection at point ‘C’ for the truss shown below. E = 200 GPa A = 2 × 10–4 m2 for all members.

Find slope at supports and at point ‘C’, deflection at ‘C’ and ‘D’ for the given beam using Macaulay’s method.

Determine the deflection and slope at the free end of cantilever beam of span ‘l’ m, loaded with central point load ‘w’ kN. E 1 is constant.