**Important RGPV Question**

Table of Contents

Toggle** CE-305 (Strength of Materials)**

**III Sem, CE**

**UNIT-1: ****Simple Stress & Strains**

**Q.1) **A steel rod of 3 cm diameter and 5 m long is coated to two grips and the rod is maintained at a temperature of 95Β°C. Determine the stress and force pull exerted when temperature falls to 30Β°C, if

i) The ends do not yield

ii) The ends yield by 0.12 cm.

Take E=2x 105 MN/mΒ² and a=12 x 10-6Β°C.

**(RGPV June 2023)**

**Q.2) **A straight bar 450 mm long is 20 mm in diameter for the first 250 mm length and 10 mm diameter for the remaining length. If the bar is subjected to an axial pull of 10kN. Find the extension of the bar. Take E=2 x 105 N/mm.

**(RGPV Nov 2022)**

**Q.3) **A steel rod of 25mm in diameter and 2 meter long is subjected to an axial pull of 45 kN. Find:

i) The intensity of stress ii) The strain Maximum Marks: 70 b ii) Elongation Take E =2 x 105 N/mm

**(RGPV Nov 2022)**

**Q.4) **A mild steel specimen is fixed at both the end as shown in fig. if load, P=30 kN and area = 5 cm2 is given. Find the maximum stress induced in the specimen.

**(RGPV Dec 2020)**

**Q.5) **Explain in detail. i) Plain Stress condition ii) Plain strain condition

**(RGPV Dec 2020)**

**Q.6) **Explain the principle of super position.

**(RGPV Dec 2020)**

**Q.7) **Write short notes on: Longitudinal and lateral strain.

**(RGPV Dec 2020)**

**Q.8) **A point is subjected to a tensile stress of 250MPa in the horizontal direction and another tensile stress of 100MPa in the vertical direction. The point is also subjected to a simple shear stress of 25MPa. Such that when it is associated with the major tensile stress, it tends to rotate the element in the clockwise direction what is the magnitude of the normal and shear stresses on a section inclined at an angle of 20**,, Β°**, with the major tensile stressβ.

**(RGPV June 2020)**

**Q.9) **Write short notes on: i) Hookeβs Law ii) Modulus of Elasticity.

**(RGPV June 2020)**

**Q.10) **A rectangular beam 60mm wide and 150mm deep is simply supported over a span of 4 meters. If the beam is subjected to a uniformly distributed load of 4.5 kN/m. Find the maximum bending stress induced in the beam.

**(RGPV June 2020)**

**Q.11) **Distinguish between Direct Stress and Bending Stress.

**(RGPV June 2020)**

**Q.12) **What do you understand by the term βPoint of contraflexureβ?

**(RGPV June 2020)**

**Q.13) **Define principal planes and principal stresses and explain their uses.

**(RGPV June 2020)**

**Q.14) **Briefly define of the following.

a) Principal Planes

b) Temperature Stresses

**(RGPV May 2019)**

**Q.15) **What do you understand by the term simple stress and strain? Also explain Mohr’s circle of stress and strain.

**(RGPV Nov 2019)**

**Q.16) **A steel tube of 4.5cm external diameter and 3mm thickness encloses centrally a solid copper bar of 3cm diameter. The bar and the tube are rigidly coected together at the ends at a temperature of 30Β°C. Find the stress in each metal when heated to 180Β°C. Also find the increase in length if the original length of the assembly is 30cm.

**(RGPV May 2018)**

**Q.17) **What is principal stress and principal strain?

**(RGPV May 2018)**

**Q.18) **At a point in a strained material the principal stress are 120N/mmΒ² (tensile) and 80N/mmΒ² (compressive). Determine the normal stress, shear stress and resultant stress on a plane inclined at 50Β° to the axis of major principal stress. Also determine the maximum shear stress at the point.

**(RGPV May 2018)**

**Q.19) **If a tension bar is found to taper uniformly from (d-a) cm diameter to (d+a) cm, prove that the error involved in using the mean (10a/d)Β² diameter to calculate Young’s modulus is percent.

**(RGPV May 2018)**

**Q.20) **Write short note on-Principal planes .

**OR**

Briefly define principal planes.

**(RGPV Dec 2017, RGPV May 2019)**

**Q.21) **Explain Mohr’s circle.

**OR**

What is the purpose of Mohr’s circle?

**(RGPV June 2015, RGPV Dec 2015)**

**Q.22) **State Hooke’s law.

**OR**

Write short note on Hooke’s law

**OR**

Define Young’s modulus of elasticity.

**OR**

Define Hooke’s law and modulus of elasticity.

**(RGPV June 2014, 2017, RGPV Nov 2018, RGPV May 2019, RGPV June 2011)**

**Q.23) **Draw and explain stress strain curve for M.S. and C.I.

**OR**

Write short note on-Draw the stress-strain diagram for ductile and brittle material.

**(RGPV Dec 2016, RGPV Nov 2018)**

**Q.24) **Define malleability and ductility.

**(RGPV Dec 2015)**

**Q.25) **Define stress and strain. Derive a relation between stress and strain.

**(RGPV June 2013)**

**Q.26) **Explain with mathematical derivation, the thermal stresses induced in a body due to change in temperature.

**OR**

Explain with mathematical derivation, thermal stresses induced in her of tapering section due to change in temperature.

**OR**

Define temperature stresses.

**OR**

Briefly define temperature stresses.

**(RGPV Dec 2011, RGPV Dec 2015, RGPV Dec 2016, RGPV May 2019)**

**Q.27) **A RCC column of size 230 x 400 mm has 8 steel bar of 12mm dia. column is subjected to an axial load of 600 N (compression), find the stress developed in steel and concrete. Take E, 18.67E.

**(RGPV Dec 2016)**

**Q.28) **Two vertical rods one of steel and the other of copper are each rigidly fixed at the top and 50 cm apart. Diameters and lengths of each rod are 2 cm and 4 m respectively. A cross bar fixed to the rods at the lower ends carries a load of 5000 N such that the cross bar remains horizontal even after loading. Find the stress in each rod and the position of the load on the bar. Take E for steel=2x 105 N/mm2 and E for copper = 1 x 105 N/mmΒ².

**(RGPV May 2018)**

**Q.29) **Define principal planes and principal stresses.

**OR**

Write short notes on-

(i) Principal plane

(ii) Principal stress.

**OR**

What is principal stress and principal strain?

**(RGPV Dec 2012, June 2014, Dec 2014, June 2015, RGPV June 2013, Nov 2018, RGPV May 2018)**

**UNIT-2: ****Bending & Shearing Stresses**

**Q.1) **A hollow steel shaft 3 m long must transmit a torque of 25 kNm. The total angle of twist in this length is not to exceed 2.5Β° and the allowable shearing stress is 90 MPa. Determine the inside and outside diameter of the shaft if G = 85 GPa.

**(RGPV June 2023)**

**Q.2) **A 120 mm x 50 mm I-Section is subjected to a shearing force of 10kN. Calculate the shear stress at the neutral axis and at the top of the web. Given I = 220 x 10 mmΒ², Area 9.4 x 102 mmΒ², web thickness=3.5 mm and flange thickness=5.5 mm.

**(RGPV June 2023)**

**Q.3) **A simply supported beam of span L, carrying a point load P at 0.3L from left support. Determine the mid-span displacements and slopes at the supports, using the method of integration.

**(RGPV June 2023)**

**Q.4) **Find the SF at left support, if a simply supported beam of span 6 m is subjected an eccentric point load of 9 KN at distance of 2 m from the left support.

**(RGPV June 2023)**

**Q.5) **Draw the S.F and B.M diagrams of the beam shown in Figure 1.

**(RGPV June 2023)**

**Q.6) **A solid shaft is to transmit 337.5 kW at 120 r.p.m. If the shear stress of the material must not exceed 80 N/mmΒ². Find the required diameter.

**(RGPV Nov 2022)**

**Q.7) **A beam of length I simply supported at the ends caries a point load What a distance a from the left end. Find the deflection under the load and the maximum deflection using Macaulay’s method.

**(RGPV Nov 2022)**

**Q.8) **Derive the relation between the rate of loading, shear force and bending moment.

**(RGPV Nov 2022)**

**Q.9) **Draw the shear force and bending moment diagrams for a beam supported and loaded as shown in figure.

**(RGPV Nov 2022)**

**Q.10) **A rectangular block of material is subjected to a tensile stress of 110 N/mmΒ² on one plane and a tensile stress of 47 N/mmΒ² on a plane at right angle, together with shear stresses of 63 N/mmΒ² on the same planes. Find: i) The direction of the principal planes. ii) The magnitude of the principal stress. iii) The magnitude of the greatest shear stress.

**(RGPV Nov 2022)**

**Q.11) **A rectangular beam 300 mm deep is simply supported over a span of 4 meters. What uniformly distributed load the beam may carry, if the bending stress is not exceed 120 MPa. Take I = 9 Γ 106 mm4.

**(RGPV Dec 2020)**

**Q.12) **Show that for a rectangular section, the distribution of shearing stress is parabolic.

**(RGPV Dec 2020)**

**Q.13) **Determine the deflection at free and of beam of constant uniform cross-section of length L. It is subjected to a concentrated load P at the free end with uniformly varying load in the full span of the beam as shown below. Also find out the slope at the free end by using STRAIN ENERGY.

**(RGPV Dec 2020)**

**Q.14) **A I-section, with rectangular ends, has following dimensions: Flanges = 150 mm Γ 20 mm Web = 300 mm Γ10 mm. Find the maximum shearing stress developed in the beam for a shear force of 50 kW.

**(RGPV Dec 2020)**

**Q.15) **A cantilever beam 2 m long is subjected to uniformly distributed load of 5 kN/m over its entire length. Find the slope and deflection of the cantilever beam at it free end Take EI = 2.5 Γ 1012 N mmΒ².

**(RGPV Dec 2020)**

**Q.16) **A cantilever 2.4m long carries a point load of 30kN at its free end. Find the slope and deflection of the cantilever under the load. Take Flexural Rigidity for the cantilever beam as 25Γ1012 N-mm2.

**(RGPV June 2020)**

**Q.17) **Give the relation between an actual beam and a conjugate beam when the former has a fixed end.

**(RGPV June 2020)**

**Q.18) **A Cantilever beam of span 4m is supported at the free end to the level of fixed end. It carries a concentrated load of 20 kN at the center of the span. Calculate the reaction at the prop and draw the S.F. and B.M. diagrams.

**(RGPV May 2019)**

**Q.19) **Derive the expression for shear stress distribution over I-section.

**(RGPV Nov 2019, Dec 2015)**

**Q.20) **A solid circular shaft is to transmit 375 kW at 150RPM. Find the diameter of the shaft of the shear stress is not to exceed 65 N/mmΒ².

**(RGPV Nov 2019)**

**Q.21) **A shearing force of 180 kN act over a T-section shown in figure 1. Draw the shear stress distribution curve. Take I = 1.134 Γ 108 mm4.

**(RGPV Nov 2019)**

**Q.22) **Deduce an expression for Pure Bending of beam equation as given below.

Where;

M = Bending Moment;

I = Moment of Inertia of beam;

f = Bending stress at a distance ‘y’ from neutral Axis;

E = Young’s modulus of Elasticity and

R = Radius of Curvature.

**OR**

Derive the expression M/IE/Ray for simple bending of a bean.

**OR**

Derive an expression for bending stress at a layer in a beam.

**(RGPV May 2019, RGPV Dec 2015, RGPV May 2018)**

**Q.23) **Explain assumptions made in simple theory of bending.

**(RGPV June 2017)**

**Q.24) **Define flexural rigidity and its significance.

**(RGPV Dec 2015, Nov 2019)**

**Q.25) **A beam is of square section of the side ‘a’. If the permissible bending stress is ‘o’, find the moment of resistance when the beam section is placed such that- (i) Two sides are horizontal (ii) One diagonal is vertical.

Find also the ratio of the moments of the resistance of the section in the two positions.

**(RGPV Dec 2016)**

**Q.26) **A reinforced concrete beam is 200 mm wide and 400 mm deep. The maximum allowable stresses in steel and concrete are 120 and 7.5 N/mm respectively. What area of steel reinforcement is required if both the stresses are developed and steel reinforcement is 60 mm above the tension face? If modular ratio m 16 determine the moment of resistance of the beam.

**(RGPV June 2015)**

**Q.27) **Define the point of contraflexure in a beam.

**(RGPV Nov 2019)**

**Q.28) **A cast iron beam has an I-section with top flange 80 mm Γ 40 mm, web 120 mm Γ 20 mm and bottom flange 160 mm x 40 mm. If tensile stress is not to exceed 30 N/mmΒ² and compressive stress 90 N/mmΒ², what is the maximum uniformly distributed load the beam can carry over a simply supported span of 6.0 metre if the larger flange is in tension?

**(RGPV June 2017)**

**Q.29) **Define shear stress and show the shear stress distribution mathematically and graphically over solid circular section.

**(RGPV Dec 2015)**

**Q.30) **A rectangular beam is to be cut from a circular log of wood of diameter D, find the dimensions of the strongest section in bending.

**(RGPV May 2018)**

**UNIT-3: ****Slope & Deflection of Beams**

**Q.1) **A circular alloy bar 2m long uniformly tapers from 30mm diameter to 20mm diameter. Calculate the elongation of the rod under an axial force of 50kN. Take E for the alloy as 140GPa.

**(RGPV June 2020)**

**Q.2) **What is a conjugate beam? Discuss its utilities.

**(RGPV June 2020)**

**Q.3) **A Simply Supported R.C. rectangular beam of span 4m and cross section 150mmx300mm is loaded as shown in figure. Find the maximum Slope and deflection of the beam. Take E=2x 104 N/mmΒ².

**(RGPV May 2019)**

**Q.4) **Write the assumption of theory of simple bending and prove the relations,

**(RGPV Nov 2019)**

**Q.5) **Short note on Define the point of contra-flexure in a beam.

**(RGPV Nov 2019)**

**Q.6) **A simply supported Beam of 3 m span carries point load of 120 kN and 80 kN a distance of 0.6m and 2 m from the left side of the support. If moment of inertia for the Beam I = 16x108mm and E-210 GN/mΒ².find the deflection under load.

**(RGPV Nov 2019)**

**Q.7) **Derive an expression for bending stress at a layer in a beam.

**(RGPV May 2018)**

**Q.8) **What is the relation between slope, deflection and radius curvature of a simple supported beam?

**(RGPV Nov 2018)**

**Q.9) **A beam of length 8m is simply supported at its ends. It carries a uniformly distributed load of 40kN/m as shown in figure. Determine the deflection of the beam at its mid-point and also the position of maximum deflection and maximum deflection. Take E-2Γ105 N/mmΒ² and I-4.3Γ108mm4.

**(RGPV May 2018)**

**Q.10) **What is the use of conjugate beam method over other methods?

**(RGPV June 2014)**

**Q.11) **A beam ABC, 8 m long carries an eccentric load at ‘B’ such that AB=3 m, BC= 5 m. If EI= 5000 kN-m2 determine- (i) Slope at ends A and C and (ii) Maximum deflection.

**(RGPV June 2015)**

**Q.12) **A simply supported beam of 6 m span is subjected to a concentrated load of 18 kN at 4.0 m from left support. Calculate- (i) The position and the value of maximum deflection (ii) Slope at mid-span (iii) Deflection at the load point.

**(RGPV June 2017)**

**Q.13) **A beam 6 m long is simply supported at ends carries a UDL of 4 kN/m throughout its length. Draw BM diagram of the beam using conjugate beam method determine the slope at the ends and deflection in the centre El is the flexural rigidity of the beam El= 10500 kN-mΒ².

**(RGPV Dec 2014)**

**UNIT-4: ****Columns and Struts & Thin Pressures Vessels**

**Q.1) **A thin spherical vessel 100mm diameter and 12.5mm thick is filled with water. More water is pumped in until the pressure reaches 4.2 MPa. How much extra water is required to reach this pressure? Assume E = 210 GPa Y = 0.25.

**(RGPV June 2023)**

**Q.2) **A compound cylinder is made by shrinking a cylindrical of external diameter 300 mm and internal diameter of 250 mm over an another cylindrical of external diameter 250 mm and internal diameter 200 mm. The radial pressure at the junction after shrinking is 8 N/mmΒ². Find the final stresses sent up across the section, when the compound cylinder is subjected to an internal fluid pressure of 84.5 N/mmΒ².

**(RGPV June 2023)**

**Q.3) **Find the Euler’s critical load for a hallow cylindrical cast iron column 200 mm external diameter and 25 mm thick, if it is 6 meter long and hinged at both ends. Take E -8x 104 N/mmΒ². Compare Euler’s Critical load with the rankine’s critical load taking fe = 550 N/mmΒ² and a =1/1600. For what length of column Euler’s critical loads by Euler’s and Rankine’s formula be equal.

**(RGPV Nov 2022)**

**Q.4) **Write short notes on: Stability

**(RGPV Dec 2020)**

**Q.5) **A steel rod 5m long and 40mm diameter is used as a column, with one end fixed and other free. Determine the crippling load by Eulerβs formula. Take E as 200GPa.

**(RGPV June 2020)**

**Q.6) **Explain the failure of long columns and short columns.

**(RGPV June 2020)**

**Q.7) **A concrete column of cross-sectional area of 350×350 mm is reinforced by four longitudinal 30mm diameter round steel bars placed at each corner. If the column carries comprehensive load of 400kN, determine comprehensive stresses produced in the concrete and steel bars. Assume that Young’s modulus of elasticity of steel is 15 times of that concrete.

**(RGPV May 2019)**

**Q.8) **What is meant by effective length of a column? Also define Slenderness Ratio.

**(RGPV May 2019)**

**Q.9) **Find an expression for crippling load for a long column when both ends of column are fixed.

**(RGPV May 2019)**

**Q.10) **List out various theories of failure. Explain any one theory of failure in detail.

**(RGPV May 2019, Nov 2019)**

**Q.11) **Short note on Differentiate column and struts.

**(RGPV Nov 2019)**

**Q.12) **Define slenderness ratio of a column. What is its importance?

**OR**

Write short note on-Slenderness ratio in long column.

**OR**

Define slenderness ratio.

**(RGPV Dec 2010, RGPV June 2013, RGPV Dec 2016)**

**Q.13) **Explain different modes of failure of a column subjected to axial load.

**(RGPV Dec 2015)**

**Q.14) **State Euler’s theory for long columns.

**OR**

Define the term crippling load.

**OR**

Define crippling load.

**(RGPV June 2014, RGPV Dec 2014)**

**Q.15) **Write short note on equivalent length of column.

**OR**

What is equivalent length of a column

**OR**

What do you mean by equivalent length of column?

**(RGPV June 2013, May 2018, RGPV June 2014, RGPV Dec 2014, June 2015)**

**Q.16) **Explain effective length and slenderness ratio.

**OR**

Explain effective length of a column and slenderness ratio.

**OR**

What is meant by effective length of a column? Also define slenderness ratio.

**(RGPV Dec 2011, RGPV Dec 2013, RGPV May 2019)**

**Q.17) **What is limiting value of the slenderness ratio beyond which Euler’s formula is applicable?

**(RGPV June 2015)**

**Q.18) **Derive the expression for Euler’s buckling load of a column having both ends hinged.

**OR**

Derive Euler equation for buckling of column hinged at both ends.

**OR**

Deduce an expression for Euler’s formula for axially loaded long column.

**(RGPV Dec 2012, RGPV June 2013, RGPV Dec 2017, Nov 2019)**

**Q.19) **What are the various end conditions for a column? Write formula for Euler’s critical load for each condition.

**OR**

What do you mean by end conditions of a column?

**(RGPV Dec 2014, RGPV June 2014)**

**Q.20) **A hollow alloy tube 4 m long with external and internal diameter of 40 mm and 25 mm respectively was found to extend 4.8 mm under a tensile load of 60 kN. Find the buckling load for the tube with both ends pied. Also find the safe load on the tube. Taking a factor of safety as 5. (A hollow alloy tube 4 m long with external and internal diameter of 40 mm and 25 mm respectively was found to extend 4.8 mm under a tensile load of 60 kN. Find the buckling load for the tube with both ends pied. Also find the safe load on the tube. Taking a factor of safety as 5.

**(RGPV Nov 2018)**

**Q.21) **What are the merits of Rankine’s load over Euler load in buckling?

**(RGPV Dec 2014, June 2015)**

**Q.22) **A hollow cast iron column 200 mm outside diameter and 150 mm inside diameter, & m long has both ends fixed it is subjected to an axial compressive load. Taking a factor of safety as 6, Ο = 560 N/mmΒ², a = 1/1600, determine the safe Rankine load.

**(RGPV Dec 2016)**

**Q.23) **Write short note on- Thin pressure vessels.

**(RGPV Dec 2017)**

**Q.24) **Derive a formula for the hoop stress in a thin spherical shell subjected to an internal pressure.

**(RGPV Nov 2018) **

**Q.25) **A cylinder of internal diameter 2.5 m and of thickness 5 cm contains a gas. If the tensile stress in the material is not to exceed 80 N/mm determine the internal pressure of the gas.

**(RGPV Dec 2016)**

**UNIT-5: ****Torsion of Shafts & Unsymmetrical Bending**

**Q.1) **A Solid steel shaft is to transmit a torque of 10 kN-m. If the shearing stress is not to exceed 45 MPa, find the minimum diameter of shaft.

**(RGPV Dec 2020)**

**Q.2) **Derive an expression for the angle of twist in the case of a member of circular cross-section subjected to torsional moment.

**(RGPV Dec 2020)**

**Q.3) **Calculate the maximum torque that a shaft of 125mm diameter can transmit, if the maximum angle of twist is 1o in a length of 1.5m. Take C = 70GPa.

**(RGPV June 2020)**

**Q.4) **A hollow shaft of external and internal diameter of 80mm and 50mm is required to transmit torque from one end to the other. What is the safe torque it can transmit, if the allowable shear stress is 45 MPa?

**(RGPV June 2020)**

**Q.5) **Write short notes on: Torque

**(RGPV June 2020)**

**Q.6) **Compare the moment of resistance of the following sections of same materials and of same cross section area of circular section and square section.

**(RGPV May 2019)**

**Q.7) **Deduce an expression for pure torsion equation with its all assumptions.

**(RGPV May 2019)**

**Q.8) **Briefly define of the following.

1)Shear Center

2) Concept of Pure Torsion.

**(RGPV May 2019)**

**Q.9) **What do you understand by pure Torsion? Also deduce an expression for pure torsion equation.

**(RGPV Nov 2019)**

**Q.10) **What do you understand by shear centre? Also write its importance.

**(RGPV Nov 2019)**

**Q.11) **Short note on Assumption for pure Torsion theory.

**(RGPV Nov 2019)**

**Q.12) **A rectangular beam is to be cut from a circular log of wood of diameter D, find the dimensions of the strongest section in bending.

**(RGPV June 2013)**

**Q.13) **Derive the expression β

where the symbol represent the usual meaning.

**OR**

Derive torsional equation.

**(RGPV June 2013, RGPV Dec 2016)**

**Q.14) **What do you mean by the torsional rigidity of the shaft? What’s its significance?

**OR**

Define torsional rigidity of a shaft. Prove that the torsional rigidity is the torque required to produce a twist of one radian in unit length of shaft.

**OR**

Explain torsional rigidity of shaft.

**(RGPV Dec 2012, RGPV June 2008, RGPV June 2015)**

**Q.15) **Determine the maximum strain energy stored in a solid shaft of diameter 10 cm and of length 1.25 metre, if the maximum allowable shear stress is 50 N/mmΒ². Take C=8 x 10 N/mmΒ².

**(RGPV June 2014)**

**Q.16) **A hollow steel shaft is made to replace a solid wrought iron shaft of the same external diameter, the material being 35 percent stronger than the iron. Find what fraction of the outside diameter the internal diameter may be. Also neglecting the couplings, find the percentage saving in weight by this substitution, assuming that steel is 2% heavier than wrought iron.

**(RGPV May 2018)**

**Q.17) **What do you understand by shear centre?

**OR**

Define shear centre.

**OR**

Write short note on – Shear centre.

**OR**

Briefly define shear centre.

**(RGPV Dec 2014, June 2015, Dec 2015, RGPV Dec 2016, RGPV Dec 2017, RGPV May 2019)**

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