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II B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 STRENGTH OF MATERIALS-I Civil Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. Design the cross section for a beam acted upon by a bending moment = 50 KNm. If width of beam is 200 mm calculate, depth. f = 9 N/mm2 . [16]

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2. Define Neutral axis. Sketch the bending stress distribution across the cross section of a rectangular beam section 230 × 400 m subjected to 60 KNm moment. [16]

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3. Rails of 15 m length were laid on the track when the temperature was 200 C. A gap of 1.8 mm was kept between two consecutive rails. At what max temperature the rails will remain stress free ? If the temperature is raised further by 150 C, what will be the magnitude and nature of stresses induced in the rails? [16]

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4. Construct the S. F. D & B. M. D for the beam with over hangs as shown in Figure ?? [16]

Figure ??

5. (a) Explain the double integration method for finding slope and deflection of beams.

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(b) A beam of 12m span is carrying a point load of 40 KN at 5m from left support. Calculate the slopes at the two supports and deflection under the load. Take EI=12 × 106 KN m2 . [8+8]

6. Derive Lame?s equations for finding the radial and hoop stresses in a thick spherical shell subjected to an internal pressure. [16]

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7. A steel bolt of 650 sq.mm C.S.A passes centrally through a copper tube of C.S.A. 1200 sq. mm. the tube is 500 mm long and is closed by rigid washers which are fastened by the threads on the steel bolt. The pitch of the thread is 3 mm. If the nut is tightened through 900 , find the stresses in the bolt and the tube. [16]

8. A cylindrical shell 1.2m long, 200mm internal diameter and 10mm thick is filled with a fluid at atmospheric pressure. If an additional 3 X 104 mm3 of the fluid is pumped into the cylinder, find the pressure exerted by the fluid on the wall of the cylinder. Find also the hoop stress induced. Take E = 2 X 105 N/mm2 , µ = 0.3.

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II B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 STRENGTH OF MATERIALS-I Civil Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Define the “Beam” and the type of action and deformation it undergoes.

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(b) Draw the S.F. and B.M. diagram for a simply supported beam of span L m loaded with UDL of w KN/m. [6+10] 2. A beam supports a maximum bending moment of 60 KNm at a section on span. The cross section dimensions are b = 230 mm, d = 400 mm. Calculate the maximum bending stresses. [16] 3. (a) Explain the Mohr’s theorems, for finding the slope and deflection of a beam.

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(b) A simply supported 6m rolled steel joist carries a U.D.L of 10 KN//m length. Determine slope and deflection at a distance of 3m from one end of the beam. [6+10]

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4. A steel cylinder of outside diameter 240 mm and inside diameter 200 mm is shrunk on to one having diameters 200 and 160 mm, the interference fit being such that under an internal pressure p, the inner tensile stress in both cylinders = 85.4N/mm2 . Find the initial difference in the nominal 200 mm diameters and the value of p if E = 2.1 × 105 N/mm2 . [16] 5. (a) State the assumptions made in the theory of simple bending. (b) Derive the simple bending equation.

[6+10]

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6. A cylindrical shell 3m long has 1m. internal diameter and 15mm metal thickness. Calculate the circumferential and longitudinal stresses induced and find out the changes in the dimensions of the shell , if it is subjected to an internal pressure of 1.5 N/mm2 . Also find out the maximum shear stress. Take E = 2 X 105 N/mm2 , µ = 0.3.

[16]

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7. A weight of 210 kN is supported by three short pillars each of sectional area 500 mm2 . The central pillar is of steel and the outer ones are of copper. The pillars are so adjusted that at a temperature of 150 C each carries equal load. The temperature is then raised to 950C. Find the stress in each pillar at 150 C and 950 C. Take Es = 200 GPa and EC = 80 GPa αs = 12 × 10−6 / 0 C and αc = 18 × 10−6 / 0 C. [16] 8. The max. pressure in a steam engine cylinder of internal dia. 30 cm is 1 MPa (gauge). Find the stress in the piston rod if it is 5 cm in dia. What is the elongation of the rod if it is 80 cm long? Take E = 200 GPa. If the allowable stress in the cover bolts is 40 N/ mm2 , find the number of 16 mm dia. bolts necessary to fasten the cover to the cylinder. Assume the core dia. of bolts as 13.835 mm. [16] 3

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II B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 STRENGTH OF MATERIALS-I Civil Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

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1. Compare the values of max. and minimum hoop stresses for a cast steel cylindrical shell of 600 mm external dia. And 400 mm internal dia. Subjected to a pressure of 30N/mm2 applied (a) Internally and (b) Externally.

[8+8]

3. Write short notes on

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(a) Moment area method

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2. Sketch the stress - strain diagram for a brittle material marking the salient points on it. How is this curve different from that of a ductile material. Explain the procedure of obtaining the yield stress of materials not having a well defined yield point. [16]

(b) Macaulay’s method

(c) Deflections of propped beams.

4. (a) With usual notation derive the bending equation :

[16] M I

=

f y

=

E R

(b) State the assumptions made in the theory of simple bending.

[16]

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5. Construct S. F. D & B. M. D for the S. S beam shown in Figure ??.

[10+6]

Figure ??

6. For triangular section (bxh) subjected to a S.F. (F), obtain the shear stress distribution. Mark the salient values. [16] 7. (a) Define the terms i. Longitudinal stress ii. Volumetric strain

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(b) A boiler shell of 2m. diameter is made up of mildsteel plates of 20mm thick. The efficiency of the longitudinal and circumferential Joints is 70% and 60% respectively. Determine the safe pressure in the boiler, if the permissible tensile stress in the plate section through the rivets is 100 N/mm2 . Also determine the circumferential stress in the solid plate section and longitudinal stress through the rivets. [4+12]

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8. Two steel bars A and B are of same length 30 cm . Bar A is of 20 mm dia. For 10 cm length and 40 mm dia. For the remaining length . Bar B is of 20 mm dia. For 20 cm length and 40 mm dia. For remaining length . An axial blow is given to bar A which produces a max. instantaneous stress of 180 /mm2 in it . Find the max instantaneous stress produced by the same axial blow on B. If each bar is stressed upto the elastic limit, find the ratio of strain - energy stored. [16]

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II B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 STRENGTH OF MATERIALS-I Civil Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

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1. Determine the changes in length, width and thickness of a steel bar 50 mm long, 25 mm wide and 15 mm thick if it is subjected to an axial pull of 40 kN. Take E = 200 GPa and Poisson?s ratio = 0.3. [16] 2. Find out the slope and deflection at free end of cantilever beam with point load at center from Mohr’s theorems. [16]

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3. A shell 3.25m. long, 1m in diameter is subjected to an internal pressure of 1N/mm2 . If the thickness of the shell is 10mm, find the circumferential and longitudinal stresses. Also find out the maximum shear stress and the changes in the dimensions of the shell. Take E = 2 × 105 N/mm2 , µ = 0.3.

[16]

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4. The internal dia. of a thick spherical shell is 200mm and the wall thickness is 50mm. Calculate the max. and minimum values of circumferential stresses due to an internal pressure of 6N/mm2 . [16]

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5. Define Bending moment and state of pure bending. Draw the B. M. D and S. F. D and identify the region of zero S.F.(Figure??) [16]

Figure ??

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6. A wagon of weight 25 k N, attached to a wire rope, is moving at speed of 4 km ph . The cross - sectional area of rope is 5 cm2 . Suddenly the rope jams and the wagon is brought to rest. If the length of the rope is 10 m at the time of sudden stoppage, find the instantaneous stress and elongation of rope if E = 200 Gpa. & g = 9.8 m/sec2 . [16] 7. For a hollow circular section obtain the section modulus. Hence calculate the maximum bending stresses in a section external radius 300 mm and internal radius 180 cm, subjected to B. M = 50 KNm. [16] 8. Derive an expression for the distribution of shear stress across the cross section. How is average shear stress defined. Relate maximum shear stress to the average shear stress in a rectangular section. [16] 7

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