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Code No: R21011 R10 SET - 1 II B. Tech I Semester Supplementary Examinations, Dec - 2014 MECHANICS OF MATERIALS (Civil Engineering) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks 1. a) Explain the different types of coplanar forces and also write their equations of equilibrium. b) A circular cylinder of weight 2.5 kN and diameter 300 mm is supported by a right angled groove as shown in Figure 1. Determine the reactions at the points of contact. Assume all surfaces are to be smooth. 300 Figure 1 2. a) State and explain the Laws of Friction. b) A ladder of length 8 m and weight 200 N is placed against a smooth vertical wall and a rough horizontal floor. The ladder is at an inclination of 60 0 with respect to horizontal. Determine the coefficient of friction of the floor to keep the ladder in equilibrium configuration. 3. An open-belt drive connects two pulleys 1 m and 0.6 m diameters, on parallel shafts 4.5 m apart. The maximum tension in the belt is 2 kN. The driver pulley of diameter 1 m runs at 225 rpm. The coefficient of friction is 0.32. Find the power transmitted and the torque on each of the two shafts. 4. Determine the directions of principal axes and the principal moments of inertia of the crosssection shown in Figure 2. 10 mm 100 mm 10 mm 75 mm Figure 2 1 of 2 |''|'||||''|''||'|'| R10 Code No: R21011 SET - 1 5. a) Draw the stress-strain diagram for mild steel and explain salient points. b) Determine the elongation of the stepped steel bar subjected to axial forces as shown in Figure 3. 2 50 kN A = 125 mm 300 mm A = 250 mm2 75 kN A = 500 mm2 450 mm 750 mm 150 kN Figure 3 6. Draw the shear force and bending moment diagrams for a beam of span 6 m supported and loaded as shown in Figure 4. 75 kN 50 kN 50 kN/ m 25 kN/ m 2m 2m Figure 4 2m 7. A simply supported beam of span 4.5 m has an I-section with flanges 150 mm wide, overall depth 250 mm, flanges12 mm thick and the thickness of web is 10 mm. Determine the intensity of the uniformly distributed load which will produce a maximum stress of 125 N /mm2. 8. A steel beam cross-section shown in Figure 5, is subjected to a shear force of 150 kN. Draw the shear stress distribution across the depth of the section. Also find the ratio of maximum shear stress and the average shear stress. 200 mm 16 mm 250 mm 12 mm 16 mm 150 mm Figure 5 2 of 2 |''|'||||''|''||'|'| Code No: R21011 R10 SET - 2 II B. Tech I Semester Supplementary Examinations, Dec - 2014 MECHANICS OF MATERIALS (Civil Engineering) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks 1. Two identical rollers, each of weight 2.25 kN, are supported by an inclined plane making an angle 600 with respect to horizontal and a vertical wall as shown in Figure1. Find the reactions at the points of contact. Assume all surfaces are to be smooth. 600 Figure 1 2. A ladder of length 6 m and weight 300 N is supported by a vertical wall and a horizontal floor. The ladder is making an angle 60 0 with respect to horizontal. A man weighing 600 N climbs the ladder. Determine the position of the man on the ladder, will cause slipping of the ladder. The coefficient of friction between all contact surfaces is 0.25. 3. An open belt running over two pulleys 300 mm and 600 mm diameters connects two parallel shafts 3.6 m apart and transmits 4.25 kW from smaller pulley that rotates at 325 rpm. The coefficient of friction between the belt and the pulleys is 0.32 and the safe working tension is 10 N/mm width. Find the minimum width of the belt and the initial tension in the belt. 4. Determine the directions of principal axes and the principal moments of inertia of the cross75 mm section shown in Figure 2. 12 mm 150 mm 12 mm 12 mm 100 mm Figure 2 1 of 2 |''|'||||''|''||'|'| R10 Code No: R21011 SET - 2 5. A solid steel bar 600 mm long and 72 mm diameter, is placed inside an aluminium tube having 75 mm inside diameter and 100 mm outside diameter. The aluminum tube is 0.25 mm longer than steel bar. An axial load of 750 kN is applied to the bar and tube through rigid cover plates. Find the stresses developed in the steel bar and aluminium tube. ESt is 2× 105 N/mm2 and EAl is 0.7× 105 N/mm2. 6. Draw the shear force and bending moment diagrams for the beam supported and loaded as shown in Figure 3. 100 kN 50 kN 2m 50 kN/ m 4m 2m Figure 3 7. A steel beam of unsymmetrical I-section, top flange 150 mm × 16 mm, web 12 mm × 225 mm and bottom flange 200 mm × 16 mm, is supported over a span of 5.2 m. If the permissible stresses are 175 N/mm2 in compression and 100 N/mm2 in tension, determine the safe uniformly distributed load carried by the beam. 8. A beam of I -section 300 mm deep and 200 mm wide, has equal flanges 20 mm thick and web 16 mm thick. It carries, at a section a shear force of 250 kN. Draw the distribution of shear stress across the section and also indicate the values at important points. Find the ratio of maximum to mean shear stress. 2 of 2 |''|'||||''|''||'|'| R10 Code No: R21011 SET - 3 II B. Tech I Semester Supplementary Examinations, Dec - 2014 MECHANICS OF MATERIALS (Civil Engineering) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks 1. Two circular cylinders, each of weight 1.5 kN and diameter 300 mm, are connected at their centers by a flexible but inextensible string of length 500 mm and rest upon a horizontal plane, supporting above them a third cylinder of weight 2.5 kN and diameter 300 mm as shown in Figure 1. Find the reactions at the various points of contact and also the force in the string. Assume all surfaces are to be smooth Figure 1 2. A force of 250 N, acting parallel to the plane, is required just to move a block up an inclined plane making an angle 180 with respect to horizontal. If the angle of inclination of the plane is changed to 220 the effort required, acting parallel to the plane is 300 N. Find the weight of the block and the coefficient of friction. 3. An open-belt drive connects two pulleys 1.5 m and 1.0 m diameters, on parallel shafts 4.5 m apart. The maximum tension in the belt is 3 kN. The driver pulley of diameter 1.5 m runs at 250 rpm. The coefficient of friction is 0.3. Find the power transmitted and the torque on each of the two shafts. 4. Determine the directions of principal axes and the principal moments of inertia of the crosssection shown in Figure 2. 12 mm 150 mm 12 mm 100 mm Figure 2 1 of 2 |''|'||||''|''||'|'| R10 Code No: R21011 SET - 3 5. A mild steel bar 25 mm in diameter and 500 mm long is encased in a brass tube having external diameter is 40 mm and internal diameter is 32 mm. The composite bar is heated through 500 C. Calculate the stresses induced in each metal. The coefficient of expansion for steel and brass are 11 × 10-6 and 16 × 10-6 per oC respectively. ESteel = 2× 105 N/mm2 and EBrass = 1× 105 N/mm2. 6. Draw the shear force and bending moment diagrams for the beam supported and loaded as shown in Figure 3. 50 kN 100 kN 25 kN/ m 1.5 m 25 kN 10 kN/ m 3m 1.5 m Figure 3 7. A simply supported beam of span 4.2 m has unsymmetrical I-section, top flange 125 mm × 12 mm, web 10 mm × 150 mm and bottom flange 150 mm × 12 mm. It carries a uniformly distributed load of 60 kN /m over its entire span. Fine the maximum tensile and compressive stresses due to bending. 8. A simply supported beam of span 4.2 m carries a uniformly distributed load of 50 kN /m over the entire span. The cross-section of the beam is a T-section having flange width 150 mm, flange thickness 16 mm, web thickness 10 mm and overall depth 200 mm. Draw the distribution of shear stress across the section and also find the ratio of maximum shear stress to the mean stress. 2 of 2 |''|'||||''|''||'|'| R10 Code No: R21011 SET - 4 II B. Tech I Semester Supplementary Examinations, Dec - 2014 MECHANICS OF MATERIALS (Civil Engineering) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks 1. a) Derive the equations of equilibrium of various types of coplanar forces. b) Find the resultant of the system of forces shown in Figure 1. Y 25 kN 15 kN 10 kN 300 600 20 kN X 450 50 kN 30 kN Figure 1 2. A flexible but inextensible string connects two blocks of weights 500 N and 1000 N. The two blocks are placed on an inclined plane and the string is parallel to the plane. The 500 N block is below the 1000 N block. The coefficient of friction between the 500 N block and the inclined plane is 0.2 and that for 1000 N block is 0.3. Find the angle of inclination of the plane and the force in the string when the motion is about to take place down the plane. 3. An open belt running over two pulleys 500 mm and 750 mm diameters connects two parallel shafts 4 m apart and transmits 5 kW from smaller pulley that rotates at 350 rpm. The coefficient of friction between the belt and the pulleys is 0.3 and the safe working tension is 12 N/mm width. Find the minimum width of the belt and the initial tension in the belt. 1 of 2 |''|'||||''|''||'|'| R10 Code No: R21011 SET - 4 4. Determine the directions of principal axes and the principal moments of inertia of the crosssection shown in Figure 2. 50 mm 10 mm 100 mm 10 mm 10 mm 75 mm Figure 2 5. a) Derive the relation between various elastic constants. b) A vertical steel rod 1000 mm long is fixed at its top and a weight of 500 N is dropped from a height of 250 mm on to a collar at the lower end. The upper 500 mm length of the rod is has a diameter of 20 mm while the reaming portion has 16 mm diameter. Determine the maximum instantaneous stress induced in the rod. 6. A simply supported beam of span 6 m carries a uniformly distributed load of 25 kN/m run over the length of left half of its span, together with concentrated loads of 25 kN, 50 kN and 75 kN situated at 1m, 2m and 3m respectively from right support. Draw the shear force and bending moment diagrams and find out the magnitude and position of the maximum bending moment. 7. A beam of T-section, flange 150 mm × 16 mm, width of the web 12 mm and overall depth of the section 200 mm is simply supported over a span 4.5 m and is so arranged that the flange is uppermost. It carries a uniformly distributed load of 50 kN/m over its entire span. Fine the maximum tensile and compressive stresses. 8. A steel beam cross-section shown in Figure 3, is subjected to a shear force of 125 kN. Draw the shear stress distribution across the depth of the section. 150 mm 12 mm 200 mm 10 mm 12 mm 125 mm Figure 3 2 of 2 |''|'||||''|''||'|'|