INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad

INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad -00 04 CIVIL ENGINEERING QUESTION BANK Course Name : STRENGTH OF MATERIALS II Course Code : A404 Class : II B. Tech II Semester Section A Branch : Civil Engineering Year : 0 0 Course Faculty : Mr. G Anand Reddy, Assistant Professor, Civil Engineering Department OBJECTIVES To impart adequate knowledge to find stresses in various structural parts used in buildings, dams, bridges, retaining walls and pressure in vessels, etc. To understand the failure phenomenon and to learn how to prevent the failure. To impart adequate knowledge to continue the design and research activity in structural analysis. PART - A (SHORT ANSWER QUESTIONS) UNIT-I Define a) Torque b) Torsional moment of resistance c) Polar section Understand modulus Define Spring constant. Differentiate and explain types of springs. Understand Derive the equation for power transmitted by a shaft. 4 Define spring and mention types of springs. Understand State functions of springs. Understand Write torsional equation and explain the terms Understand & Remember 7 Derive the expression for torque transmitted by a hollow shaft Write the Polar Modulus (i) for a solid shaft and (ii) for a hollow shaft. Remember 9 Why hollow circular shafts are preferred when compared to solid circular Analyze shafts? 0 Write the equation for strain energy stored in a shaft due to torsion. Remember What are the assumptions made in theory of pure torsion? Remember Explain combined bending and torsion Remember Define polar modulus and sectional modulus Remember 4 State the theories of failure according to elastic theory Remember Write the equations for deflection in close and open coiled helical springs Remember under Axial load and couple What is strain Energy? Remember 7 Explain Tensional Stiffness Remember Draw and Explain the parameters of different types of springs Remember 9 Derive Spring Stiffness and Shear stress in springs Remember P a g e

0 Explain Springs in series and in parallel Remember UNIT-II Define column and effective length of a column. Distinguish between a column and a strut. Understand Distinguish between short column and long column. Understand Define slenderness ratio, crippling load. Understand 4 Explain the Limitations of Euler s Formula? Understand What are the assumptions made in Euler s theory to arrive at buckling load on column. Calculate the slenderness ratio of a strut made from a hollow tube of 0mm outside diameter, mm inside diameter and.m long. 7 A steel strut is 0.m diameter and m long. It is built in rigidly at bottom but completely unrestrained at the top. Calculate the buckling load taking E=0GPa. Understand & Remember Write short notes on curved beams and explain its uses. Understand & 4 Remember 9 State the different types of supports and provide the relation between Remember 4 effective length and actual length of column 0 Explain the expression of crippling load in case of both end fixed condition With the figure Explain the expression of crippling load in case of both end hinged condition With the figure Explain the expression of crippling load in case of one end fixed and other Remember 4 hinged condition With the figure Explain the expression of crippling load in case of one end fixed and other Remember 4 free condition With the figure 4 Explain Slenderness ratio for different types of columns Remember 4 Define radius of gyration Understand State the limitations of eulers theory Understand 7 State Straight line formula Understand Explain Prof Perry s Formula Understand 9 Derive Rankine Gordon formula Understand 0 Explain the failure criteria in columns UNIT-III Define beam columns. Understand What is the effect of lateral load on the bucking of columns? Understand What is meant by equivalent length of a column? Understand 4 Write the expression for maximum deflection, maximum bending moment and maximum stress of a beam-column simply supported and carrying a UDL of intensity w per unit length. Write the expression for maximum deflection, maximum bending moment and maximum stress of a beam-column simply supported at ends and carrying a concentrated load at centre. Understand Write short notes on eccentric loading Understand 7 Write short note on retaining wall. Understand Understand State the importance of middle third rule in gravity dams. & Remember 9 Understand Distinguish between active and passive earth pressures. & Remember 0 Derive an expression for resultant stress of a masonry dam. Give the practical examples of curved beams State and explain the combined stresses on action of direct loading and Understand P a g e

bending moment Define beam column. Give an Example Understand 4 Write short note on earth pressure Understand What is active earth pressure. Understand What are laterally loaded struts. Understand 7 What are the different types of earth pressure. Understand What is passive earth pressure. Understand 9 Write short note on chimney with neat sketch. Understand 0 Write short note on dam. Understand UNIT-V Write short note on centroid? Understand 7 Write short motes on principal axes. Understand 7 Explain parallel axis theorem for product of inertia. Understand 7 4 Define ellipse of inertia. Understand 7 Write short notes on unsymmetrical bending. Understand 7 Define Flexure or bending axis. Understand 7 7 Write short note on shear centre. Understand 7 Explain unsymmetrical bending 7 9 Explain flexure or bending axis 7 0 Determine the shear centre of symmetrical section shown below. 7 Write short note on moment of inertia. Understand 7 Explain product of inertia. Understand 7 Write equation of ellipse and locus of a point. Understand 7 4 Define combined bending and axial loads. Understand 7 Write an expression for combined bending and axial load. 7 define the expressions for shear centre of symmetrical sections 7 7 Derive expression for unsymmetrical bending. Understand 7 Write the expressions for shear centre for Equal leg angle sections 7 9 Define deflection of beams under unsymmetrical bending. Understand 7 0 Explain the expressions for shear centre for channel sections. 7 UNIT-V Distinguish between thin cylinder and thick cylinder? Understand Write short note on longitudinal stress? Understand Write the maximum value of shear stress in thin cylinder. Remember & Understand 4 What are assumptions made in the analysis of thin cylinders? Remember & Understand Define shrinkage allowance. Understand Write short notes on compound cylinders. Understand 7 Write equations for radial stress as per Lame s theory Remember 9 Write short notes on lames theory for thick cylinders with assumptions. Understand 9 9 What are the different methods of reducing hoop stresses? Remember & 9 Understand 0 Define hoop stress? Understand Distinguish between hoop and longitudinal stress? Understand Define thin cylinder with neat sketch? Understand Write boundary conditions for compound cylinders. Understand 4 Define thick cylinder with neat sketch? Understand Write are the assumptions for lames theory for thick cylinders. Understand Explain difference of radii for shrinkage. Understand 7 Write equations for hoops stress as per Lame s theory Remember 9 P a g e

Write assumptions of lames theory for thick cylinders. Understand 9 9 Define thick spherical shell. Understand 0 Derive expression for volumetric strain of cylindrical shells. 9 PART - B (LONG ANSWER QUESTIONS) 4 Differentiate and explain types of springs. UNIT-I Calculate the maximum stress in a propeller shaft with a 400mm external and 00mm internal diameter, when subjected to a twisting moment of 40Nm. If the modulus of rigidity, C=GN/m, how much is the twist in a length 0 times the diameter? a) Explain the theory of pure torsion with assumptions. b) Define solid length, spring rate, pitch A closed coil cylindrical spring of circular cross-section has coils with a 7mm mean diameter. When loaded with an axial load of 0N, it is found to extend 0mm and when subjected to a twisting couple of Nm, there is an angular rotation of 0 degrees. Determine the poisons ratio for the material. a)define spring index (C). (m) b) Derive the stiffness of springs with sketches when arranged in series & Remember & Understand evaluate analyze evaluate creating Understand parallel. Determine the diameter of a solid steel shaft which will transmit.kw at 00rpm. Also determine the length of the shaft if the twist must not exceed. 0 over the entire length. The maximum shear stress is limited to N/mm. Take G = x0 4 N/mm 7 Derive the expression for torque transmitted by a hollow shaft Apply 9 0 The internal diameter of a hollow shaft is / rd of its external diameter. Compare its resistance to torsion with that of solid shaft of the same weight and material. a) Distinguish between close and open helical coil springs b) What is the value (i) maximum shear forces (ii) central deflection in a leaf spring subjected to an axial force? c) Write the equation for the deflection of an open coiled helical spring subjected to an axial load W. A hollow shaft of diameter ratio / is required to transmit 00kW at 0rpm. The maximum torque being 0% greater than the mean. The shear stress is not to exceed MPa and the twist in a length of m is not to exceed.4 0. Calculate the minimum external diameter satisfying theses conditions. Apply Analyze Creating Derive the relation between Twisting moment, Shear stress and angle of twist Apply A propeller shaft 0mm in diameter transmits.mw at 0rpm. The propeller weighs 0kN and overhangs its support by 400mm. If the propeller Analyze thrust is of kn weights. Calculate the maximum principal stress induced in the cross-section and indicates its position. C=0MPa 4 Derive expression equations for strength and stiffness of a circular shaft when an external torque T is acting on it. A solid shaft of diameter d is subjected to an axial thrust P and an axial torque of T. Show that the principal stresses at a point on the surface of the Creating 4 P a g e

shaft is given by Derive expressions for polar modulus for a hollow circular shaft Analyze Find the mean radius of an open coiled spring (helix angle is 0 0 ) to give a vertical displacement and an angular rotation of the loaded end 0.0 radian Analyze under an axial load 40N. The material available is a steel rod of mm ` diameter. E= 0GPa. C=0GPa 7 Derive expression for strain energy for a solid circular shaft Apply A composite spring has two close coiled helical spring connected in series, each spring has coils at a mean diameter of cms. Find the diameter of the wire in one of the springs if the diameter of wire in other spring is mm and the stiffness of the composite is 700N/m. 9 Derive expression for strain energy for a hollow circular shaft Apply In a open coil helical spring having 0 coils, the stresses due to bending and twisting are 9MPa and 0MPa respectively, and the spring is axially Analyze 0 loaded. Assuming the mean diameter of the coils to be times the diameter of wire, find the maximum permissible load and the diameter of wire for a maximum extension of cm. E=0GPa and G=GPa. UNIT-II Derive the equivalent length of a column whose both ends are hinged using apply Euler s theory. A tabular steel strut is cm external diameter and cm internal diameter, m long and has hinged ends. This is subjected to eccentric lad. Find the maximum eccentricity for crippling load of 0% of the Euler s load. The yield stress being 00MPa and E=00GPa. Remember Derive the equivalent length of a column for which one end is fixed and other evaluate end hinged using Euler s theory. A hollow circular steel strut with its ends position fixed, has a length of m, external diameter of 0.4m and internal diameter 0cm. Before loading, the 4 strut is bent with a maximum deviation of 0.4cm. Assuming the central line to be sinusoidal, determine (a) the maximum stress due to a central compressive end load of kn. (B) If the load has an eccentricity of.cm, then find the maximum stress induced. Take E = 00GPa Understand Derive the equivalent length of a column for which both ends are fixed using creating Euler s theory. A steel strut of circular cross-section.m long is hinged at both ends. Find the necessary diameter in order that if a thrust of 0kN deviates at the end by /0 th of the diameter from the axis of the strut, the greatest compressive stress shall not exceed MPa. If the yield stress of steel 00MPa, find the crippling load. E = 00GPa Remember 7 Derive the equivalent length of a column for which one end is fixed and other apply end is free using Euler s theory. A steel column is of rectangular cross-section 4cm X cm and is having initial curvature given by. T carries a compressive load of 0kN at the hinged ends. (a)find the maximum resultant stress induced on Understand 4 either side of the column. (b) If this load is having an eccentricity of.cm, then also find the stresses. E = 00GPa 9 Derive Rankine s formula analyze 0 What is the ratio of strength of a solid steel column of 0mm diameter to that of a hollow circular steel column of the same cross-sectional area and a wall thickness of mm? The two columns have the same length and have pinned ends. apply P a g e

Explain the limitations of Euler s theory apply Determine the safe axial load a timber column of cross-sectional area 0mm X 0mm and of 4m length can carry using a factor of safety,. Take E = 0kN/mm and for (a)hinged ends (b) fixed ends (c)one end free and other end fixed (d)one end hinged and other end fixed. Remember 4 7 9 0 Derive the maximum and minimum stresses developed in eccentrically loaded long columns From the Euler s crushing load for a hollow cylindrical cast iron column, 0mm external diameter and 0mm thick, if it is m long and hinged at both ends. Compare this load with that obtained by the Rankines formula using constants 0N/mm and /00. For what length of the column would these two formulae give the same crushing loads? E for the material = 0kN/mm Derive the equation for maximum deflection and stresses for a uniformly loaded lateral strut. A steel column consists of two channels ISMC 00 X. kg/m placed back to back at a clear distance of cm and two plates of 0mm X 0mm are connected to the flanges. Find the crippling load for the column if the distance between the hinged ends is m. Take E = 0kN/mm. Properties of channel sections: Area of cross-section of each channel = 4.4cm I xx =. cm 4 I yy = 0. cm 4 C yy =. cm Thickness of web = 7.mm Thickness of flange =.mm Derive the maximum bending moment, maximum shear force for a circular beam loaded uniformly and supported on symmetrically placed columns A steel strut of circular section is m long and hinged at both ends. Find the necessary diameter such that under a thrust of 00kN at an eccentricity of 0. of the diameter from the axis of the strut, the maximum compressive stress does not exceed 90kN/mm. If the yield tress in compression for steel is 400N/mm, find the crippling load of the strut. analyze apply analyze 4 Remember 4 evaluate 4 apply 4 Derive the maximum bending moment for a semi-circular beam simply supported on three supports spaced equally. apply A cast iron column with a 0cm external diameter and cm internal diameter is m long. Calculate the safe load using Rankine s formula if a) both ends hinged (b) both ends fixed (c) one end free and other end fixed (d) one end apply 4 hinged and other end fixed. σ c = 00N/mm, α = /00. Adopt factor of safety of. UNIT-III Derive the equation for maximum bending moment of a strut subjected to compressive axial load and a transverse point load at centre and whose both ends are pinned. Creating &analyze A propeller shaft of 0cm external diameter and cm internal diameter has to transmit 0.kW at 00rpm. It is additionally subjected to a bending moment of 0kNm and an end thrust of 00kN. Find i) principal stresses and their planes and ii) maximum shear stress and it plane. Derive the equation for maximum deflection of a strut subjected to compressive axial load and a transverse point load at centre and whose both ends are pinned. P a g e

4 A masonry dam of rectangular section, 0m high and 0m wide, as water up to a height of m on its one side. Find a) Pressure force due to water and m length of dam b) Position of centre of pressure and the point at which the resultant cuts the base. Take weight density of masonry=9.kn/ m and of water =9.kN/ m. Calculate the maximum and minimum stress intensities at base of dam. Derive the equation for maximum stress of a strut subjected to compressive axial load and a transverse point load at centre and whose both ends are pinned. Understand 7 A brick chimney weighs 00kN and has internal and external diameters at the base are m and m respectively. The chimney leans by ⁰ with the vertical. Calculate the maximum stresses in the base. Assume that there is no wind pressure and C.G of chimney is m above the base. Derive the equation for maximum bending moment of a strut subjected to compressive axial load and a transverse point load at centre and whose both ends are fixed. Remember & evaluate Analyze 9 Determine the maximum stress induced in a cylindrical steel strut of length.m and diameter 0mm. The strut is hinged at both ends and subjected to an axial thrust of 0kN at its ends and a transverse point load of.kn at the centre. E=0GPa. Derive the equation for maximum deflection of a strut subjected to compressive axial load and a transverse point load at centre and whose both ends are fixed. 0 Determine the maximum stress induced in a horizontal strut of length.m and of rectangular cross section 40mm wide and 0mm deep when it carries an axial thrust of 00kN and a vertical load of kn/m length. The strut is having pin joints at its ends. E=0GPa. Derive the earth pressure of a retaining wall when a) Earth pressure at rest Remember & evaluate b) When a outthrust of intensity, p acts at the horizontal surface of earth c) When earth is surcharged The line of thrust, in a compression testing specimen mm diameter, is parallel to the axis of the specimen but is displaced from it. Calculate the Analyse distance of the line of thrust from the axis when the maximum stress is 0% greater than the main stress on a normal section. Derive the resultant stress for masonry dams A short column of additional diameter 40cm and internal diameter 0cm 4 carries an eccentric load of 0kN. Find the greatest eccentricity which the load can have without producing tension on the cross section. Write the expressions for direct stress, bending stress, torsional stress and Remember 7 P a g e

principal stresses when a body is under combined effect of axial, bending and torsional stresses. Also derive equation for equivalent torque. 7 9 A short column of rectangular cross section 0mm X 0mm carries a load of 40kN at a point 0mm from the longer side and mm from the shorter side. Determine the maximum compressive and tensile stresses in the section. Explain middle - third rule for rectangular sections A trapezoidal masonry dam having 4m top width, m bottom width and m high, is retaining water up to a height of 0m. The density of masonry is 000kg/ m. The coefficient of friction between dam and soil is 0.. The allowable compressive stress is 40N/m. Check the stability of dams. Derive the maximum and minimum compressive stresses in masonry Chimneys Understand Remember & Understand 0 A masonry retaining wall of trapezoidal section is m high and retains earth which is level up to the top. The width at the top is m and at the bottom is m and exposed face is vertical. Find the maximum and minimum intensities of normal stress at the base. Take density of earth=00kg/m and density of masonry=00kg/ m and angle of repose of earth=0 0 UNIT-IV Derive the equation for shear centre of channel section. Understand 7 A rectangular beam is cm wide and 0cm deep. It is used as a simply supported beam on a span of m. Two loads of kn each are applied to the beam, each load being m from a support. The plane of loads makes an angle of 0⁰ with the vertical plane of symmetry. Find the direction of neutral axis and maximum bending stresses at Point A as shown in figure below. 0cm N V P A U Understand 7 cm Explain the stresses developed due to unsymmetrical bending. 7 4 A simply supported beam T-section,.m long carries a central concentrated load inclined at 0⁰ to the Y-axis. If the maximum compressive and tensile stresses are not to exceed 7MPa respectively find the maximum load the Apply 7 beam can carry. Derive the deflections of straight beam subjected to unsymmetrical bending. 7 A standard I-beam is bent by equal and opposite couples M acting at the ends of the beam in the plane m-m. Find the maximum stress and the maximum Apply 7 deflection. I=400mm 4, Iv=0cm 4, M=kNm, l=m, ϕ=0 0, E= 00GPa 7 Explain briefly about shear centre for symmetrical sections. Apply 7 Find the moment of inertia of unequal leg angle iron section as shown in figure with respect to axis passing through the centroid. Remember 7 P a g e

9 Derive the resultant shear force, F R for equal leg angle section. 7 A beam is loaded as shown in figure. Determine the maximum deflection and stress at B. 0 Creating 7 Derive the shear centre for channel section Apply 7 A cantilever beam of I-section is used to support the loads inclined to the V- axis as shown in figure. Calculate the stresses at the corners A, B, C and D. Also locate the neutral axis. Remember 7 Derive shear centre for unequal I-section Understand 7 4 A cantilever beam has a channel section as shown in the figure. A concentrated load kn lies in the plane of the laods making an angle of 0 0 with the X-axis. Load,P lies in the plane of the cross section of the free end of the beam and passes through shear centre,c. Locate points of maximum tensile and compressive stresses in the beam and determine their magnitudes. Remember 7 9 P a g e

Explain Mohr s circle of inertia with a neat sketch 7 A channel section is loaded as shown in the figure. Determine (a) the product of inertia with respect to x and y axes; (b) Shear centre. Remember 7 7 Explain (a) Principal axes and (b) ellipse of inertia with neat sketches 7 A steel bar of rectangular section cm X 4cm is arranged as a cantilever projecting horizontally 0cm beyond the support. The broad face of the bar makes 0 0 with the horizontal. A load of 00N is hung from the free end. Find the neutral axis, the horizontal and vertical deflections of free end, and the maximum tensile stress. 9 Derive transformation laws for moment and product of inertia. Analyze 7 0 Locate the shear centre of the unsymmetrical section as shown in the figure. apply 7 0 P a g e

4 7 9 UNIT-V Derive the stresses developed in thin cylindrical vessel subjected to internal pressure. Apply A steel water pipe 0.m in diameter has to resist the pressure due to a head of 0m of water. To what thickness should it e made if the working intensity of pressure in the metal is to be N/mm. After the pipe has lost.mm of its creating thickness due to corrosion. Take the specific weight of water to be 0kN/m Derive expression for longitudinal stress and maximum shear stress developed in thin cylindrical vessel due to internal pressure. Find the circumferential stress at the inner and outer radius respectively in the case of a pipe with a 00mm internal diameter and which is 40mm thick Remember when subjected to an internal pressure of 7.N/mm Derive circumferential strain and longitudinal strain for a thin cylindrical shell subjected to internal pressure A thick cylinder of steel having an internal diameter of 00mm and an external diameter of 00mm is subjected to an internal pressure of N/mm Remember and an external pressure of 7N/mm. Find the maximum hoop stress. Derive volumetric strain for a thin cylindrical shell subjected to internal pressure A thick cylindrical pipe of outside diameter 00mm and thickness of metal 0mm is subjected to an internal fluid pressure of 40N/mm and an external pressure of 4N/mm. Calculate the maximum and minimum intensities of Remember circumferential and radial stresses in the pipe section. Show that when a thin walled spherical vessel of dia 'd' and thickness 't' is subjected to internal fluid pressure 'p', the increase in volume equal to Apply 0 A compressed air cylinder for laboratory use ordinarily carries approximately N/mm pressure at the time of delivery. The outside diameter of such a cylinder is 0mm. If the steel has a yield point of N/mm and a safety factor of. Calculate the required wall thickness. Derive the stresses developed in thick cylindrical vessel subjected to internal fluid pressure. A cast iron pipe having an internal diameter of 0cm has wall mm thick and is closely wound with a single layer of steel wire mm diameter under a stress of MN/m.Calculate the stresses in pipe and the wire when the internal pressure in the pipe is MPa. apply Analyze Remember P a g e

4 7 9 0 Derive the hoop stress developed in thick cylindrical vessel subjected to internal fluid pressure alone. A cast iron pipe having an internal diameter of 0cm has wall mm thick and is closely wound with a single layer of steel wire mm diameter under a stress of MN/m. Calculate the stresses in the pipe and the wire when the internal pressure in the pipe is MPa. E s = 00GPa and E CI = 00GPa What do you mean by thick compound cylinders? How will you determine the hoop stresses in a thick compound cylinder? A cylindrical steel vessel with hemispherical ends is 0cm long over all, the outside diameter is 0cm and the thickness mm throughout. Calculate the change in internal volume of the vessel when it is subjected to an internal pressure of MPa. E=00GPa and υ = 0. What are the different methods of reducing hoop stress? Explain the terms: wire winding of thin cylinders and shrinking of one cylinder over the another cylinder. A copper tube of inside diameter cm and outside diameter.cm is closely wound with steel wire of diameter mm. Find the tension at which the wire must be wound on the tube if a pressure of.mpa is required before the copper is subjected to tensile stresses, the tube being free to expand or contract axially. For copper, E c =0GPa, υ=0., and for steel, E s =00GPa Derive an expression for the radial pressure and hoop stress for thick spherical shell. A cylindrical pressure vessel with closed ends is cm external diameter and mm thick. It is wound closely with a single layer of circular section steel wire of.mm diameter under tension of 9MN/m. If the cylinder is treated as thin, calculate the (a) initial stress in cylinder, (b) initial pressure which will produce a stress of 4MN/m, and (c) stress in the wire under these conditions. Poisson s ratio = 0.0 Apply apply Apply Apply Analyze evaluate Apply Understand HOD, CIVIL ENGINEERING P a g e