**CE1259 STRENGTH OF MATERIALS**

**UNIT I**

**STRESS STRAIN DEFORMATION OF SOLIDS**

**PART- A (2 Marks)**

**1. What is Hooke’s Law?**

**2. What are the Elastic Constants?**

**3. Define Poisson’s Ratio.**

**4. Define: Resilience, proof resilience and modulus of resilience.**

**5. Distinguish between rigid and deformable bodies.**

**6. Define stress and strain.**

**7. Define Shear stress and Shear strain.**

**8. Define elastic limit.**

**9. Define volumetric strain.**

**10. Define tensile stress and compressive stress.**

**11. Define young’s Modulus.**

**12. Define modulus of rigidity.**

**13. Define thermal stress.**

**PART- B (16 Marks)**

**1. A rod of 150 cm long and diameter 2.0cm is subjected to an axial pull of 20 KN. If the**

**modulus of elasticity of the material of the rod is 2x 105 N/mm2**

**Determine 1. Stress 2. Strain**

**3. the elongation of the rod (16)**

**2. The extension in a rectangular steel bar of length 400mm and thickness 10mm is found to**

**0.21mm .The bar tapers uniformly in width from 100mm to 50mm. If E for the bar is 2x 105**

**N/mm2 ,Determine the axial load on the bar (16)**

**3. A rod of 250 cm long and diameter 3.0cm is subjected to an axial pull of 30 KN. If the**

**modulus of elasticity of the material of the rod is 2x 105 N/mm2 Determine 1. Stress 2. Strain**

**3. the elongation of the rod (16)**

**4. Find the young’s modulus of a rod of diameter 30mm and of length 300mm which is**

**subjected to a tensile load of 60 KN and the extension of the rod is equal to 0.4 mm**

**(16)**

**5. The extension in a rectangular steel bar of length 400mm and thickness 3mm is found be**

**0.21mm .The bar tapers uniformly in width from 20mm to 60mm E for the bar is 2x 105**

**N/mm2 Determine the axial load on the bar. (16)**

**6. The ultimate stress for a hollow steel column which carries an axial load of 2Mn is 500**

**N/mm2 .If the external diameter of the column is 250mm, determine the internal diameter**

**Take the factor of safety as 4.0 (16)**

**UNIT II**

**BEAMS – LOADS AND STRESSES**

**PART- A (2 Marks)**

**1. State the different types of supports.**

**2. What is cantilever beam?**

**3. Write the equation for the simple bending theory.**

**4. What do you mean by the point of contraflexure?**

**5. Define beam.**

**6. Define shear force and bending moment.**

**7. What is Shear stress diagram?**

**8. What is Bending moment diagram?**

**9. What are the types of load?**

**10. Write the assumption in the theory of simple bending.**

**11. What are the types of beams?**

**12. When will bending moment is maximum.**

**PART- B (16 Marks)**

**1. Three planks of each 50 x200 mm timber are built up to a symmetrical I section for a**

**beam. The maximum shear force over the beam is 4KN. Propose an alternate rectangular**

**section of the same material so that the maximum shear stress developed is same in both**

**sections. Assume then width of the section to be 2/3 of the depth. (16)**

**2. A beam of uniform section 10 m long carries a udl of KN/m for the entire length and a**

**concentrated load of 10 KN at right end. The beam is freely supported at the left end. Find**

**the position of the second support so that the maximum bending moment in the beam is as**

**minimum as possible. Also compute the maximum bending moment (16)**

**3. A beam of size 150 mm wide, 250 mm deep carries a uniformly distributed load of w kN/m**

**over entire span of 4 m. A concentrated load 1 kN is acting at a distance of 1.2 m from the**

**left support. If the bending stress at a section 1.8 m from the left support is not to exceed**

**3.25 N/mm2 find the load w. (16)**

**4. A cantilever of 2m length carries a point load of 20 KN at 0.8 m from the fixed end and**

**another point of 5 KN at the free end. In addition, a u.d.l. of 15 KN/m is spread over the**

**entire length of the cantilever. Draw the S.F.D, and B.M.D. (16)**

**5. A Simply supported beam of effective span 6 m carries three point loads of 30 KN, 25 KN**

**and 40 KN at 1m, 3m and 4.5m respectively from the left support. Draw the SFD and BMD.**

**Indicating values at salient points. (16)**

**6. A Simply supported beam of length 6 metres carries a udl of 20KN/m throughout its**

**length and a point of 30 KN at 2 metres from the right support. Draw the shear force and**

**bending moment diagram. Also find the position and magnitude of maximum Bending**

**moment. (16)**

**7. A Simply supported beam 6 metre span carries udl of 20 KN/m for left half of span and**

**two point loads of 25 KN end 35 KN at 4 m and 5 m from left support. Find maximum SF**

**and BM and their location drawing SF and BM diagrams. (16)**

**UNIT III**

**TORSION**

**PART-A (2 Marks)**

**1. Define torsional rigidity of the solid circular shaft.**

**2. Distinguish between closed coil helical spring and open coil helical spring**

**3. What is meant by composite shaft?**

**4. What is called Twisting moment?**

**5. What is Polar Modulus ?**

**6. Define: Torsional rigidity of a shaft.**

**7. What do mean by strength of a shaft?**

**8. Write down the equation for Wahl factor.**

**9. Define: Torsional stiffness.**

**10. What are springs? Name the two important types.**

**PART- B (16 Marks)**

**1. Determine the diameter of a solid shaft which will transmit 300 KN at 250 rpm. The**

**maximum shear stress should not exceed 30 N/mm2 and twist should not be more than 10 in**

**a shaft length 2m. Take modulus of rigidity = 1x 105N/mm2. (16)**

**2. The stiffness of the closed coil helical spring at mean diameter 20 cm is made of 3 cm**

**diameter rod and has 16 turns. A weight of 3 KN is dropped on this spring. Find the height**

**by which the weight should be dropped before striking the spring so that the spring may be**

**compressed by 18 cm. Take C= 8x104 N/mm2. (16)**

**3. It is required to design a closed coiled helical spring which shall deflect 1mm under an**

**axial load of 100 N at a shear stress of 90 Mpa. The spring is to be made of round wire**

**having shear modulus of 0.8 x 105 Mpa. The mean diameter of the coil is 10 times that of**

**the coil wire. Find the diameter and length of the wire. (16)**

**4. A steel shaft ABCD having a total length of 2400 mm is contributed by three different**

**sections as follows. The portion AB is hollow having outside and inside diameters 80 mm**

**and 50 mm respectively, BC is solid and 80 mm diameter. CD is also solid and 70 mm**

**diameter. If the angle of twist is same for each section, determine the length of each portion**

**and the total angle of twist. Maximum permissible shear stress is 50 Mpa and shear**

**modulus 0.82 x 105 MPa (16)**

**5. The stiffness of close coiled helical spring is 1.5 N/mm of compression under a maximum**

**load of 60 N. The maximum shear stress in the wire of the spring is 125 N/mm2. The solid**

**length of the spring (when the coils are touching) is 50 mm. Find the diameter of coil,**

**diameter of wire and number of coils. C = 4.5 (16)**

**UNIT IV**

**BEAM DEFLECTION**

**PART-A (2 Marks)**

**1. What are the advantages of Macaulay method over the double integration method, for**

**finding the slope and deflections of beams?**

**2. State the limitations of Euler’s formula.**

**3. Define crippling load.**

**4. State Mohr’s theorem.**

**5. State any three assumption made in Euler’s column theory.**

**6. What are the different modes of failures of a column?**

**7. Write down the Rankine formula for columns.**

**8. What is effective or equivalent length of column?**

**9. Define Slenderness Ratio.**

**10. Define the terms column and strut.**

**PART- B (16 Marks)**

**1. A simply supported beam of 10 m span carries a uniformly distributed load of 1 kN/m over**

**the entire span. Using Castigliano’s theorem, find the slope at the ends. EI = 30,000 kN/m2.**

**(16)**

**2. A 2m long cantilever made of steel tube of section 150 mm external diameter and10mm**

**thick is loaded. If E=200 GN/m2 calculate (1) The value of W so that the maximum bending**

**stress is 150 MN/m (2) The maximum deflection for the loading (16)**

**3. A beam of length of 10 m is simply supported at its ends and carries two point loads of**

**100 KN and 60 KN at a distance of 2 m and 5 m respectively from the left support.**

**Calculate the deflections under each load. Find also the maximum deflection.**

**Take I = 18 X 108 mm4 and E = 2 X 105. (16)**

**4. i) A column of solid circular section, 12 cm diameter, 3.6 m long is hinged at both ends.**

**Rankine’s constant is 1 / 1600 and c**

**= 54 KN/cm2. Find the buckling load.**

**ii) If another column of the same length, end conditions and rankine constant but of**

**12 cm X 12 cm square cross-section, and different material, has the same buckling load,**

**find the value of c of its material. (16)**

**5. A beam of length of 6 m is simply supported at its ends. It carries a uniformly distributed**

**load of 10 KN/m as shown in figure. Determine the deflection of the beam at its mid-point**

**and also the position and the maximum deflection. Take EI=4.5 X 108 N/mm2. (16)**

**6. An overhanging beam ABC is loaded as shown is figure. Determine the deflection of the**

**beam at point C. Take I = 5 X 108 mm4 and E = 2 X 105 N/mm2. (16)**

**7. A cantilever of length 2 m carries a uniformly distributed load of 2.5 KN/m run for a length**

**of 1.25 m from the fixed end and a point load of 1 KN at the free end. Find the deflection at**

**the free end if the section is rectangular 12 cm wide and 24 cm deep and E=1 X 104 N/mm2**

**(16)**

**8. A cantilever of length 2m carries a uniformly distributed load 2 KN/m over a length of 1m**

**from the free end, and a point load of 1 KN at the free end. Find the slope and deflection at**

**the free end if E = 2.1 X 105 N/mm2 and I = 6.667 X 107 mm4 . (16)**

**9. Determine the section of a hollow C.I. cylindrical column 5 m long with ends firmly built in.**

**The column has to carry an axial compressive load of 588.6 KN. The internal diameter of**

**the column is 0.75 times the external diameter. Use Rankine’s constants.**

**a = 1 / 1600, c**

**= 57.58 KN/cm2 and F.O.S = 6. (16)**

**UNIT V**

**ANALYSIS OF STRESSES IN TWO DIMENSIONS**

**PART-A (2 Marks)**

**1. Distinguish between thick and thin cylinders.**

**2. Define Principal planes and principal stress.**

**3. Define: Thin cylinders. Name the stresses set up in a thin cylinder subjected to internal**

**fluid pressure.**

**4. What is Mohr’s circle & name any the situations where it is used?**

**5. Define principal planes and principal stresses.**

**6. Draw Mohr’s Circle for given shear stress q.**

**7. What is the necessary condition for maximum shear stress?**

**8. Define Obliquity.**

**9. Define Strain energy and resilience.**

**10. Define proof resilience and modulus of resilience.**

**PART- B (16 Marks)**

**1. A Thin cylindrical shell 3 m long has 1m internal diameter and 15 mm metal thickness.**

**Calculate the circumferential and longitudinal stresses induced and also the change in the**

**dimensions of the shell, if it is subjected to an internal pressure of1.5 N/mm2 Take E = 2x105**

**N/mm2 and poison’s ratio =0.3. Also calculate change in volume. (16)**

**2. A closed cylindrical vessel made of steel plates 4 mm thick with plane ends, carries fluid**

**under pressure of 3 N/mm2 The diameter of the cylinder is 25cm and length is 75 cm.**

**Calculate the longitudinal and hoop stresses in the cylinder wall and determine the change**

**in diameter, length and Volume of the cylinder. Take E =2.1x105 N/mm2 and 1/m = 0.286.**

**(16)**

**3. A rectangular block of material is subjected to a tensile stress of 110 N/mm2 on one plane**

**and a tensile stress of 47 N/mm2 on the plane at right angle to the former plane and a tensile**

**stress of 47 N/mm2 on the plane at right angle to the former. Each of the above stress is**

**accompanied by a shear stress of 63 N/mm2 Find (i) The direction and magnitude of each of**

**the principal stress (ii) Magnitude of greatest shear stress (16)**

**4. At a point in a strained material, the principal stresses are100 N/mm2 (T) and 40 N/mm2**

**(C). Determine the resultant stress in magnitude and direction in a plane inclined at 600 to**

**the axis of major principal stress. What is the maximum intensity of shear stress in the**

**material at the point? (16)**

**5. A rectangular block of material is subjected to a tensile stress of 210 N/mm2 on one plane**

**and a tensile stress of 28 N/mm2 on the plane at right angle to the former plane and a tensile**

**stress of 28 N/mm2 on the plane at right angle to the former. Each of the above stress is**

**accompanied by a shear stress of 53 N/mm2 Find (i) The direction and magnitude of each of**

**the principal stress (ii) Magnitude of greatest shear stress (16)**

**6 A closed cylindrical vessel made of steel plates 5 mm thick with plane ends, carries fluid**

**under pressure of 6 N/mm2 The diameter of the cylinder is 35cm and length is 85 cm.**

**Calculate the longitudinal and hoop stresses in the cylinder wall and determine the change**

**in diameter, length and Volume of the cylinder. Take E =2.1x105 N/mm2 and 1/m = 0.286.**

**(16)**

**7. At a point in a strained material, the principal stresses are 200 N/mm2 (T) and 60 N/mm2**

**(C) Determine the direction and magnitude in a plane inclined at 600 to the axis of major**

**principal stress. What is the maximum intensity of shear stress in the material at the point**

**(16)**

**8. At a point in a strained material, the principal stresses are 100 N/mm2 (T) and 40 N/mm2**

**(C) Determine the direction and magnitude in a plane inclined at 600 to the axis of major**

**principal stress. What is the maximum intensity of shear stress in the material at the point**

**(16)**