Code No: A109210103 R09 Set No. 2 II B.Tech I Semester Examinations,December 2011 STRENGTH OF MATERIALS-I Civil Engineering Time: 3 hours Max Marks: 75 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) State and explain the Hooke’s law. (b) Draw the stress-strain diagram for mild steel and explain salient points. (c) Write the relations between Modulus of Elasticity and Shear Modulus, Mod- ulus fo Elasticity and Bulk Modulus and hence derive the relation among the three elastic constants. [15] 2. Determine the maximum pressure a mild steel water pipeline of 2 m diameter and 10 m thickness can sustain for an allowable stress of 140 MPa. Determine the change in the volume of the pipe per meter length under the maximum pressure. Assume E = 210 GPa and poisons ratio = 0.30. [15] 3. A cast iron hub of 200 mm external diameter and 100 mm thickness is pressed on to a steel shaft of 75 mm diameter. Determine the radial stress required at the interface so that the shaft can transmit 740 MW at 630 rpm. Compute the necessary diametral interference and the stresses in the shaft and the hub. If the shaft is subjected to a compressive force of 180 kN, find the change in the stresses. Assume a frictional coefficient of 0.33, Poisson’s ratio of 0.30, and Young’s modulii of steel and cast iron to be 210 GPa and 180 GPa, respectively. [15] 4. A simply supported steel beam of inverted T-section is 4.5 m long. It has 1.0 m over-hang at one end and carries a uniformly distributed load of intensity 20 kN/m on its entire span. The T section has flanges 5t × t and web t × 4t, where t is the thickness of the section. Determine the dimension t of the section if the maximum stress is limited to 165 N/mm 2 . [15] 5. A beam of I - section 250 mm deep and 150 mm wide, has equal flanges 12.5 mm thick and web 10 mm thick carries a uniformly distributed load of intensity ‘w’ as shown in figure 1. Determine the maximum value of ‘w’ at which the shearing stress and the flexural stress will attain their allowable values 110 MPa and 165 MPa, respectively. [15] Figure 1: 1
Transcript
Code No: A109210103 R09 Set No. 2
II B.Tech I Semester Examinations,December 2011STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. (a) State and explain the Hooke’s law.
(b) Draw the stress-strain diagram for mild steel and explain salient points.
(c) Write the relations between Modulus of Elasticity and Shear Modulus, Mod-ulus fo Elasticity and Bulk Modulus and hence derive the relation among thethree elastic constants. [15]
2. Determine the maximum pressure a mild steel water pipeline of 2 m diameter and10 m thickness can sustain for an allowable stress of 140 MPa. Determine thechange in the volume of the pipe per meter length under the maximum pressure.Assume E = 210 GPa and poisons ratio = 0.30. [15]
3. A cast iron hub of 200 mm external diameter and 100 mm thickness is pressedon to a steel shaft of 75 mm diameter. Determine the radial stress required atthe interface so that the shaft can transmit 740 MW at 630 rpm. Compute thenecessary diametral interference and the stresses in the shaft and the hub. If theshaft is subjected to a compressive force of 180 kN, find the change in the stresses.Assume a frictional coefficient of 0.33, Poisson’s ratio of 0.30, and Young’s moduliiof steel and cast iron to be 210 GPa and 180 GPa, respectively. [15]
4. A simply supported steel beam of inverted T-section is 4.5 m long. It has 1.0 mover-hang at one end and carries a uniformly distributed load of intensity 20 kN/mon its entire span. The T section has flanges 5t × t and web t × 4t, wheret is the thickness of the section. Determine the dimension t of the section if themaximum stress is limited to 165 N/mm2. [15]
5. A beam of I - section 250 mm deep and 150 mm wide, has equal flanges 12.5 mmthick and web 10 mm thick carries a uniformly distributed load of intensity ‘w’as shown in figure 1. Determine the maximum value of ‘w’ at which the shearingstress and the flexural stress will attain their allowable values 110 MPa and 165MPa, respectively. [15]
II B.Tech I Semester Examinations,December 2011STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. (a) Determine the maximum deflection δ in a simply supported beam of lengthL carrying a concentrated load of 5P at mid span. Use double integrationmethod.
(b) Determine the maximum deflection δ in a simply supported beam of lengthL carrying a uniformly distributed load from center of the beam to left handsupport. Use moment area method. [15]
2. Determine the maximum pressure a mild steel water pipe line of 0.30 m diameterand 3 mm thickness can sustain for an allowable stress of 120 MPa. Determine thechange in the volume of the pipe per metre length under the maximum pressure.Assume E = 210 GPa and Poisson’s ratio = 0.30. [15]
3. A weight W falls from a height of 25 mm on to a collar attached to the lowerend of a vertical steel bar 2.5 m long and 28 mm in diameter. If the maximuminstantaneous elongation is 2.5 mm, determine the corresponding stress and theweight W . [15]
4. When a certain thin-walled tube is subjected to internal pressure and torque thestresses in the tube wall are
(a) 60 N/mm2 tensile
(b) 30 N/mm2 tensile in a direction at right angles to (a)
(c) Complementary shear stress of 45 N/mm2 in the directions of (a) and (b).
Calculate the normal and tangential stresses on the two planes which are equallyinclined to (a) and (b). What are the results if due to an end thrust, (b) is com-pressive (a) and (c) being unchanged? [15]
5. A beam, shown in figure 4, carries a concentrated load W and a total uniformlydistributed load of 4W as if the bending stresses are limited to 100 N /mm2 incompression and 60 N /mm2 in tension, determine the safe uniformly distributedload carried by the beam. [15]
6. A simply supported beam of span 6 m carries a uniformly distributed load of 50kN/m over the left half of its span and 100 kN/m over the right half of its span.Draw the shear force and bending moment diagrams. Also indicate the salientpoints. [15]
7. At a certain section of a beam is subjected to a shear force F. Derive the formulaefor the shear stress at a distance y from the neutral axis, if the cross-section of thebeam is
(a) rectangle b × d
(b) a circle, diameter, D
Also determine the ratio of maximum to mean shear stress in each case. [15]
8. The cylinder for a hydraulic press has an inside diameter of 300 mm. Determinethe wall thickness required if the cylinder is to withstand an internal pressure of 40MPa without exceeding a shearing stress of 80 MPa. [15]
II B.Tech I Semester Examinations,December 2011STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. (a) Explain Macaulay’s method of beam deflection analysis, and discuss its ad-vantages over the direct integration method.
(b) Compute the maximum slope and deflection in a simple supported beam of6.0m span with a central load P = 45 kN. The beam comprises ISMB (Ix =86.04 × 106 mm4) with E = 200 Gpa. [15]
2. (a) At a point the principal stresses are 140 N/mm2 and 75 N/mm2 both tensile.Find the normal and tangential stresses on a plane inclined at 600 to the axisof the major principal stress.
(b) The principal stresses at a certain point in strained material are 150 N/mm2
and 48 N/mm2 both tensile. Find the normal and tangential stresses on aplane inclined at 20 with the major principal plane. [15]
3. Show that a solid cylinder subjected to uniform radial pressure on its surface de-velops constant hoop stresses. [15]
4. A steel hoop shrunk onto a hollow steel tube exerts a contact pressure of 20 MN/m2
on the tube. An internal pressure of 70 MN/m2 is tehn applied to the tube. Theinner and outer radii of the tube are 40 mm and 60 mm and 60mm and 100 mmfor the hoop. Determine the maximum tangential stress in the tube
(a) before the internal pressure is applied
(b) after the internal pressure is applied [15]
5. A vertical pole of height 8 m has square section throughout, the dimensions being125 mm × 125 mm at the base and uniformly tapering to 50 mm × 50 mm at thetop. A horizontal force of 10 kN is applied at the top along the diagonal of thesection. Determine the maximum bending stress induced in the section. [15]
6. A bar of 3l mm diameter and 1.5 m long has a collar at one end. It is suspendedvertically with the collar at the lower end, and a load of 25 kN is gradually droppedto the collar producing an extension in the bar of 0.5 mm. Find the height of fallif the maximum tensile stress in the bar is to be 100 N/mm2. [15]
7. Draw the shear force and bending moment diagrams for a beam supported andloaded as shown in figure 5. Locate the salient points. [15]
8. An equilateral triangular beam section with base 250 mm is subjected to a shearforce of 150 kN. Draw the distribution of the shear stress across the section andalso determine the average shear stress. [15]
II B.Tech I Semester Examinations,December 2011STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. At a point in strained material the principal stresses are 60 N/mm2 and 40 N/mm2.Find the position of plane across which the resultant stress is most inclined to thenormal and determine the value of this stress. [15]
2. Draw the shear force and bending moment diagrams for a simply supported beamloaded as shown in figure 2. Show the location of point of contraflexure. [15]
Figure 2:
3. A pressurized cylinder of 360 mm internal diameter and 3 mm wall thickness reg-istered a pressure of 0.15 MPa when subjected to an axial compression of 63 kN.Determine the poisons ratio of the material. Assume E = 150 GPa for the cylinderand K = 2.5 GPa for the fluid. [15]
4. A vertical steel rod 2.0 m long is fixed at its upper end and a weight is droppedfrom a height of 300 mm on to a collar at the lower end, produces a maximum stressof 160 N/mm2. Determine the stress in the rod if the load is applied gradually.Derive the expression involved. [15]
5. Determine the depth of the rectangular beam of width 75 mm of a beam loadedand supported as shown in figure 5. [15]
6. (a) Determine the minimum flexural rigidity of a cantilever beam so that the spanto maximum deflection ratio is not less than 250, and the slope does not exceed0.003 radian, when supporting udl of 10 kNm−1 over a span of 7.4 m.
(b) Determine the mid-span displacements and slopes at the supports in the beamsshown in figure 6b using the method of integration. Assume constant flexuralrigidity for the beams. [15]
7. Determine the magnitude and the location of the maximum shearing stress devel-oped in a beam with a cross-section shown in figure 7. due to the action of a shearforce V . [15]
Figure 7:
8. Develop the expressions for forces in spherical shells subjected to
II B.Tech I Semester Examinations,May 2011STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. A compound cylinder is designed with an interfacial radial pressure of 8 MPa. De-termine the diametral interference, and the final stresses under an internal pressureof 30 MPa. The diameters of the cylinder are 120 mm, 180 mm and 225 mm. Com-pute the maximum allowable internal pressure so that the maximum stress doesnot exceed 150 MPa. Assume E = 210 GPa. [15]
2. At a point in a beam section there is a longitudinal bending stress of 120N/mm2
tensile and a transverse shear stress of 50 N/mm2. Find the resultant stress on aplane inclined at 300 to the longitudinal axis. [15]
3. Find the elongation of a bar, length L and cross-sectional area A, under the actionof its own weight. Assume the unit weight of the bar is w/unit length. [15]
4. A concrete pipe of radius 1.0 m and 100 mm wall thickness is pre-stressed by awire 5 mm diameter to withstand a working pressure of 1.0 MPa. Determine theminimum initial stress required in the wire so that the pipe is not subjected totensile stresses under the applied pressure. Assume Ec = 25 GPa, and Es = 225GPa. [15]
5. A simply supported box-beam with an overhang supports the loads shown in thefigure 5. Determine the maximum value of load W at which the shearing stress andthe flexural stress will not exceed their allowable values 2.5 N/mm2 and 25 N/mm2,respectively. [15]
Figure 5:
6. A simply supported beam of T - section shown in figure 6. carries a uniformlydistributed load of intensity 20 kN /m on its entire 5 m span. Determine the width
of the flange of the section so that the permissible stress 50 N/mm2 in compressionand 125 N/mm2 in tension are reached simultaneously. [15]
Figure 6:
7. (a) Explain Macaulay’s method of beam deflection analysis, and discuss its ad-vantages the direct integration method.
(b) Determine the mid-span displacements and slopes at the supports in the beamsshown in figure 7 using the method of moment area. [15]
Figure 7:
8. Draw the shear force and bending moment diagrams for a simply supported beamof span 4.5 m subjected to loading as shown in figure 8. Locate the salient points.
II B.Tech I Semester Examinations,May 2011STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. Determine the width of the inverted T-beam section shown in figure 1. So that thenormal stresses at top and bottom of the beam will be in the ratio 3:1 respectively.
[15]
Figure 1:
2. A timber beam of 4.5 m span is subjected to the loading shown in figure 2. If thedepth of the beam is twice the width, design the section of the beam for flexure andshear. The permissible stresses are 25 N/mm2 in flexure and 3 N/mm2 in shear.
[15]
Figure 2:
3. (a) Explain elastic material and plastic material.
(b) Derive the relation between the modulus of elasticity and modulus of rigidityfrom first principle. [15]
4. A cylindrical boiler of diameter 1.7 m, 4.5 m length and 10 mm thickness with flatends is provided with six tie rods of 50 mm diameter. If the tie rods are stressed
initially to 100 MPa, determine the stresses in the tie rods and the cylinder undera pressure of 1.7 MPa. Assume the same material for the boiler and tie rods. [15]
5. Draw the shear force and bending moment diagrams for a beam supported andloaded as shown in figure 5. Locate the salient points. [15]
Figure 5:
6. At a point in an elastic material, a direct tensile stress of 60 N/mm2 and a directcompressive stress of 40 N/mm2 are applied on planes at right angles to each other.If the maximum principal stress is limited to 75 N/mm2 (tensile), find the shearstress that may be allowed on the planes. Also determine the minimum principalstress and the maximum shear stress. [15]
7. Determine the maximum deflection δ and slope in a simply supported beam oflength 16m carrying a concentrated load of P at 5m from right hand side and beamis also carrying a uniformly distributed load of 8 kN/m for the entire span. [15]
8. Design a spherical concrete dome over a circular opening of 7.2 m diameter tosustain a crown load of 500 kN. Allowable stresses are 5 MPa in compression and0.5 MPa in tension. [15]
II B.Tech I Semester Examinations,May 2011STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. (a) Derive the formula for horizontal shearing stress from first principles.
(b) Derive the relation between horizontal and vertical shearing stresses. [15]
2. (a) What are the advantages of compound cylinders? Explain analytically.
(b) What are the advantages and disadvantages of shell structures? [15]
3. The maximum allowable stress in a cylinder of 700 mm inner diameter and 150mm thickness is 6.3 MPa. Determine the maximum allowable internal and externalpressures on the cylinder, when applied separately. [15]
4. At a point in strained material the principal stresses are 60 N/mm2 and 40 N/mm2.Find the position of plane across which the resultant stress is most inclined to thenormal and determine the value of this stress. [15]
5. For a given permissible stress, compare the moments of resistance of a beam ofsquare section placed
(a) with two sides horizontal
(b) with a diagonal horizontal. [15]
6. (a) The left half of a beam has flexural rigidity twice that of its right half. De-termine the beam deflection profile when subjected to a u.d.l covering the lefthalf of the span.
(b) Determine the mid-span displacements and slopes at the supports in the beamsshown in figure 6 using the method of integration. [15]
7. A beam 6 m long carries a uniformly distributed load of 25 kN/m. The beam issimply supported at left-hand end and at a point distant x from the right-handend. Determine the value of x if the mid-point of the beam is to be a pointof contraflexure and for this position draw the shear force and bending momentdiagrams. [15]
8. A steel tube 32 mm external diameter and 20 mm internal diameter encloses acopper rod 16 mm diameter to which it is rigidly joined at each end. If, at atemperature of 300 C there is no longitudinal stresses. Calculate the stresses inthe rod and the tube when the temperature is raised to 1600 C. The coefficient ofexpansion for steel and copper are 11 × 10−6 and 18 × 10−6 per degree centigraderespectively. E = 2.1 × 105 N/mm2 for steel and 1.0 × 105 N/mm2 for copper.
II B.Tech I Semester Examinations,May 2011STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. The volume of a hollow cylinder of 800 mm diameter, 1.4 m length and 10 mmthickness increases by 1245 ml when subjected to an internal pressure of 4.5 MPa.Determine the Poissons ratio of the material, if E = 190.0 GPa. [15]
2. (a) The plate of a boiler is subjected to principal stresses of 120 N/mm2 and60 N/mm2 both tensile. Find the intensity of stress which acting alone willproduce the same maximum strain. Take Poisson’s ratio = 0.3.
(b) A rectangular steel bar is subjected to a tensile stress of 80 N/mm2 as well asa shear stress of 30 N/mm2. Determine the principal stresses and the principalplanes. Find also what stress acting alone can produce the same maximumstrain. Take 1 = 0.31. [15]
3. (a) Determine the maximum deflection δ in a simply supported beam of length Lcarrying a concentrated load of P at mid span. Use moment area method.
(b) Determine the maximum deflection δ in a simply supported beam of lengthL carrying a uniformly distributed load through out the length. Use doubleintegration method. [15]
4. Draw the shear force and bending moment diagrams for a beam supported andloaded as shown in figure 4. Also find maximum bending moment. [15]
Figure 4:
5. Design a cylinder of 1.8 m diameter to sustain an internal pressure of 35 MPaassuming a permissible stress of 230 MPa and Poisson’s ratio of 0.25. Apply thickcylinder theory. [15]
6. A simply supported beam 125 mm wide and 200 mm deep and 6 m long carriesa uniformly distributed load of 5 kN/m. Determine the shear stress developed at
horizontal layers 60 mm apart from top to bottom for a section 1.5 m from the rightsupport. Also determine the maximum shearing stress developed in the beam. [15]
7. Three rods, each initially of 20 mm in diameter and 2.0 m long, support a loadof 100 kN. The center rod is made of steel and the outer ones of copper. If thetemperature of the rods is increased by 1000 C and the rods are so adjusted thatthey are extended by equal amounts, determine the load carried by each rod. Thecoefficient of expansion for steel and copper are 12 × 10−6 and 18 × 10−6 per degreecentigrade respectively. E = 210 GN/m2 for steel and 85 GN/m2 for copper. [15]
8. A vertical mast of 12 m high tapers linearly from 250 mm diameter at base to 100mm at the top. At what point will the mast break under a horizontal load at thetop? If the ultimate strength of the material of the mast is 40 N /mm2, calculatethe magnitude of the failure load. [15]
II B.Tech I Semester Examinations,May/June 2012STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. A steel bar 1.5 m long and 36 mm diameter is subjected to an axial energy of 10Nm. Determine the tensile stress in the bar. If the same rod machined down to20 mm diameter in the middle half of the bar, calculate the corresponding tensilestress in the bar. [15]
2. (a) State the assumptions made in the theory of pure bending.
(b) Derive the flexure formula from first principle. [15]
3. (a) Determine the mid-span displacements and slopes at the supports in the beamsshown in figure 1 using the method of integration.
Figure 1:
(b) Determine the mid-span displacements and slopes at the supports in the beamsshown in figure 2 using the method of moment area. Assume constant flexuralrigidity for the beams. [15]
4. Draw the shear force and bending moment diagrams for a simply supported beamloaded as shown in figure 3. Also find and show the magnitude of maximum bendingmoment. [15]
5. A beam of I-section 300 mm deep and 150 mm wide. The flanges are 10 mm thickand web thickness is 8 mm. At a section the beam is subjected to a shear forceof 150 kN. Determine the proportions in which the flanges and the web resist theapplied shear. [15]
6. Plot a curve showing the percentage increase in maximum σt over average σt forratios of thickness to inside radius of thick-walled cylinders varying from 0 to 3.
[15]
7. (a) At a point the principal stresses are 150 N/mm2 and 75 N/mm2 both tensile.Find the normal and tangential stresses on a plane inclined at 600 to the axisof the major principal stress.
(b) The principal stresses at a certain point in strained material are 160 N/mm2
and 48 N/mm2 both tensile. Find the normal and tangential stresses on aplane inclined at 20 with the major principal plane. [15]
8. (a) Derive the expressions for stresses in a thin spherical shell under radial pres-sure.
(b) List the assumptions of thin cylinder theory, and explain the limitations ofthe theory. [15]
II B.Tech I Semester Examinations,May/June 2012STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. A concrete pipe of radius 1 m and 100 mm wall thickness is pre-stressed by a wire 5mm diameter to withstand a working pressure of 1 MPa. Determine the minimuminitial stress required in the wire so that the pipe is not subjected to tensile stressesunder the applied pressure. Assume Ec = 30 GPa, and Es = 200 GPa [15]
2. A simply supported beam 6 m long is subjected to a clockwise moment of 25 kNm at4.5 m from the left end, a concentrated load of 75 kN and an uniformly distributedload of 25 kN/m run over the left half of its span. Draw the shear force and bendingmoment diagrams. Mark the locations of points of inflection. [15]
3. (a) Explain working stress and factor of safety.
(b) Derive the relation between various Elastic Constants from first principle. [15]
4. Compute the stresses in a ferro-cement spherical dome of radius 5.0 m, 30.0 mmthickness and 600 semi-central angle, when subjected to
(a) self-weight
(b) snow load of 2.5 kPa. [15]
5. The shear force acting at a section of a beam is 75 kN. The section of the beam is ofT-shape of dimensions 100 mm × 150 mm × 12 mm. Determine the shear stressat the neutral axis and also draw the shear stress distribution across the section.
[15]
6. A beam of unsymmetrical I-section shown in figure 6 is simply supported over aspan of 4.5 m Determine the uniformly distributed load that the beam cancarry if the permissible stress is 162.5 N/mm2. [15]
7. (a) The plate of a boiler is subjected to principal stresses of 120 N/mm2 and60 N/mm2 both tensile. Find the intensity of stress which acting alone willproduce the same maximum strain. Take Poisson’s ratio = 0.3.
(b) A rectangular steel bar is subjected to a tensile stress of 80 N/mm2 as well asa shear stress of 30 N/mm2. Determine the principal stresses and the principalplanes. Find also what stress acting alone can produce the same maximumstrain. Take 1
m= 0.31. [15]
8. (a) Determine the maximum deflection δ in a simply supported beam of length12 m carrying a concentrated load of 250 kN at 3 m from right hand side andalso carrying a uniformly distributed load of 6 kNfor the entire span. UseMacaulay’s method.
(b) Determine the maximum deflection δ in a simply supported beam of length Lcarrying a uniformly distributed load from center of the beam to right handsupport. Use moment area method. [15]
II B.Tech I Semester Examinations,May/June 2012STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. Determine the elongation of a conical bar, length L and diameter at base D, underthe action of its own weight, assume the density of the material is ρ. [15]
2. A simply supported steel beam of span 6 m has I-section 350 mm deep and 165 mmwide has flanges 9.8 mm thick and web 7.0 mm thick. If the maximum permissiblestress is 165 N/mm2, find the safe uniformly distributed load that the section cancarry. [15]
3. At a certain point in a piece of elastic material there are normal stresses of 48N/mm2 tensile and 32 N/mm2 compressive on two planes at right angles to oneanother, together with shearing stresses of 24 N/mm2 on the same planes. If theloading on the material is increased so that the stresses reach K times those given.Find the maximum value of K if the maximum direct stress in the material is not toexceed 128 N/mm2 and the maximum shearing stress is not to exceed 80 N/mm2.
[15]
4. A cylindrical boiler of 2 m diameter, 7.2 m length and 16 mm thickness with flatends is provided with six tie rods of 50 mm diameter. If the tie rods are stressedinitially to 200 MPa, determine the stresses in the tie rods and the cylinder undera pressure of 3.6 MPa. Assume the same material for the boiler and tie rods. [15]
5. Determine the length of overhang of the beam a as shown in figure 5, such that deflectionat the free ends of the beam is zero. [15]
Figure 5:
6. Draw the shear force and bending moment diagrams for a simply supported beamloaded as shown in figure 6. Also find and show value of maximum bending moment.
7. Compute the stresses in a ferro-cement spherical dome of radius 5 m, 30 mm thick-ness and 600 semi-central angle, when subjected to
(a) crown load of 180 kN
(b) snow load of 2.5 kPa. [15]
8. A beam of triangular section base b and height h is subjected to a shear force F.Find the ratio of maximum shear stress to the shear stress at neutral axis. Alsodetermine the ratio of maximum shear stress to the mean shear stress. [15]
II B.Tech I Semester Examinations,May/June 2012STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. A circular beam of 150 mm diameter is subjected to a shear force of 25 kN. De-termine the maximum shear stress, average shear stress and the shear stress at adistance of 25 mm from neutral axis. [15]
2. (a) Determine the maximum values of slope and deflection in a cantilever of span3.8 m, if it carries a load of 20.0 kN at the free end and 50.0 kN at 1.0 m fromthe free end. Assume EI = 120.0 MNm2.
(b) Determine the mid-span displacements and slopes at the supports in the beamsshown in figure 2 using the method of moment area. Assume constant flexuralrigidity for the beams. [15]
Figure 2:
3. Find the moment of resistance of a square beam cross-section if one of its diagonalis placed vertical. Assume the cross-sectional area is 2500 mm2 and the permissiblebending stress is 40 N /mm2. [15]
4. A compound cylinder comprises an inner tube of diameters 350 mm and 450 mm,and an outer tube of diameters 400 mm and 500 mm. determine the diametralinterference required so that the final maximum stress in the tube does not exceed180 MPa under an internal pressure of 55 MPa. Neglect the effects of longitudinalstresses. Assume E = 250 GPa. [15]
5. Direct stresses of 100 N/m2 (tensile) and 90 N/mm2 (compressive) exist on twoperpendicular planes at a certain point in a body. They are also accompanied byshear stresses on the planes. The greater principal stress at the point due to theseis 150 N/mm2,
(b) Find also the maximum shear stress at the point. [15]
6. A composite bar consists of a steel rod 3 m long and 25 mm diameter encased in acopper tube 25 mm internal diameter and 32 mm external diameter. A weight of10 kN is dropped from a height of 20 mm on to a collar fixed at the bottom end ofthe composite bar. Calculate the maximum instantaneous stresses induced in thetwo components. Assume E = 200 GN/m2 for steel and 100 GN/m2 for copper.
[15]
7. A pressurised cylinder of 450 mm internal diameter and 6 mm wall thickness reg-istered a pressure fall of 0.21 MPa when subjected to an axial tension of 470.0 kN.Determine the poisons ratio of the material. Assume E = 210 GPa for the cylinderand K = 2.9 GPa for the fluid. [15]
8. A prismatic beam of weight W, length L rests on two simple supports A and B,A being at one end. Find the position of B which gives the least value of themaximum bending moment. For this position find the reactions, the maximumbending moment and the point of contra flexure. [15]
II B.Tech I Semester Examinations,May/June 2012STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. A steel bar 1.5 m long and 36 mm diameter is subjected to an axial energy of 10Nm. Determine the tensile stress in the bar. If the same rod machined down to20 mm diameter in the middle half of the bar, calculate the corresponding tensilestress in the bar. [15]
2. (a) State the assumptions made in the theory of pure bending.
(b) Derive the flexure formula from first principle. [15]
3. (a) Determine the mid-span displacements and slopes at the supports in the beamsshown in figure 1 using the method of integration.
Figure 1:
(b) Determine the mid-span displacements and slopes at the supports in the beamsshown in figure 2 using the method of moment area. Assume constant flexuralrigidity for the beams. [15]
4. Draw the shear force and bending moment diagrams for a simply supported beamloaded as shown in figure 3. Also find and show the magnitude of maximum bendingmoment. [15]
5. A beam of I-section 300 mm deep and 150 mm wide. The flanges are 10 mm thickand web thickness is 8 mm. At a section the beam is subjected to a shear forceof 150 kN. Determine the proportions in which the flanges and the web resist theapplied shear. [15]
6. Plot a curve showing the percentage increase in maximum σt over average σt forratios of thickness to inside radius of thick-walled cylinders varying from 0 to 3.
[15]
7. (a) At a point the principal stresses are 150 N/mm2 and 75 N/mm2 both tensile.Find the normal and tangential stresses on a plane inclined at 600 to the axisof the major principal stress.
(b) The principal stresses at a certain point in strained material are 160 N/mm2
and 48 N/mm2 both tensile. Find the normal and tangential stresses on aplane inclined at 20 with the major principal plane. [15]
8. (a) Derive the expressions for stresses in a thin spherical shell under radial pres-sure.
(b) List the assumptions of thin cylinder theory, and explain the limitations ofthe theory. [15]
II B.Tech I Semester Examinations,May/June 2012STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. A concrete pipe of radius 1 m and 100 mm wall thickness is pre-stressed by a wire 5mm diameter to withstand a working pressure of 1 MPa. Determine the minimuminitial stress required in the wire so that the pipe is not subjected to tensile stressesunder the applied pressure. Assume Ec = 30 GPa, and Es = 200 GPa [15]
2. A simply supported beam 6 m long is subjected to a clockwise moment of 25 kNm at4.5 m from the left end, a concentrated load of 75 kN and an uniformly distributedload of 25 kN/m run over the left half of its span. Draw the shear force and bendingmoment diagrams. Mark the locations of points of inflection. [15]
3. (a) Explain working stress and factor of safety.
(b) Derive the relation between various Elastic Constants from first principle. [15]
4. Compute the stresses in a ferro-cement spherical dome of radius 5.0 m, 30.0 mmthickness and 600 semi-central angle, when subjected to
(a) self-weight
(b) snow load of 2.5 kPa. [15]
5. The shear force acting at a section of a beam is 75 kN. The section of the beam is ofT-shape of dimensions 100 mm × 150 mm × 12 mm. Determine the shear stressat the neutral axis and also draw the shear stress distribution across the section.
[15]
6. A beam of unsymmetrical I-section shown in figure 6 is simply supported over aspan of 4.5 m Determine the uniformly distributed load that the beam cancarry if the permissible stress is 162.5 N/mm2. [15]
7. (a) The plate of a boiler is subjected to principal stresses of 120 N/mm2 and60 N/mm2 both tensile. Find the intensity of stress which acting alone willproduce the same maximum strain. Take Poisson’s ratio = 0.3.
(b) A rectangular steel bar is subjected to a tensile stress of 80 N/mm2 as well asa shear stress of 30 N/mm2. Determine the principal stresses and the principalplanes. Find also what stress acting alone can produce the same maximumstrain. Take 1
m= 0.31. [15]
8. (a) Determine the maximum deflection δ in a simply supported beam of length12 m carrying a concentrated load of 250 kN at 3 m from right hand side andalso carrying a uniformly distributed load of 6 kNfor the entire span. UseMacaulay’s method.
(b) Determine the maximum deflection δ in a simply supported beam of length Lcarrying a uniformly distributed load from center of the beam to right handsupport. Use moment area method. [15]
II B.Tech I Semester Examinations,May/June 2012STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. Determine the elongation of a conical bar, length L and diameter at base D, underthe action of its own weight, assume the density of the material is ρ. [15]
2. A simply supported steel beam of span 6 m has I-section 350 mm deep and 165 mmwide has flanges 9.8 mm thick and web 7.0 mm thick. If the maximum permissiblestress is 165 N/mm2, find the safe uniformly distributed load that the section cancarry. [15]
3. At a certain point in a piece of elastic material there are normal stresses of 48N/mm2 tensile and 32 N/mm2 compressive on two planes at right angles to oneanother, together with shearing stresses of 24 N/mm2 on the same planes. If theloading on the material is increased so that the stresses reach K times those given.Find the maximum value of K if the maximum direct stress in the material is not toexceed 128 N/mm2 and the maximum shearing stress is not to exceed 80 N/mm2.
[15]
4. A cylindrical boiler of 2 m diameter, 7.2 m length and 16 mm thickness with flatends is provided with six tie rods of 50 mm diameter. If the tie rods are stressedinitially to 200 MPa, determine the stresses in the tie rods and the cylinder undera pressure of 3.6 MPa. Assume the same material for the boiler and tie rods. [15]
5. Determine the length of overhang of the beam a as shown in figure 5, such that deflectionat the free ends of the beam is zero. [15]
Figure 5:
6. Draw the shear force and bending moment diagrams for a simply supported beamloaded as shown in figure 6. Also find and show value of maximum bending moment.
7. Compute the stresses in a ferro-cement spherical dome of radius 5 m, 30 mm thick-ness and 600 semi-central angle, when subjected to
(a) crown load of 180 kN
(b) snow load of 2.5 kPa. [15]
8. A beam of triangular section base b and height h is subjected to a shear force F.Find the ratio of maximum shear stress to the shear stress at neutral axis. Alsodetermine the ratio of maximum shear stress to the mean shear stress. [15]
II B.Tech I Semester Examinations,May/June 2012STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. A circular beam of 150 mm diameter is subjected to a shear force of 25 kN. De-termine the maximum shear stress, average shear stress and the shear stress at adistance of 25 mm from neutral axis. [15]
2. (a) Determine the maximum values of slope and deflection in a cantilever of span3.8 m, if it carries a load of 20.0 kN at the free end and 50.0 kN at 1.0 m fromthe free end. Assume EI = 120.0 MNm2.
(b) Determine the mid-span displacements and slopes at the supports in the beamsshown in figure 2 using the method of moment area. Assume constant flexuralrigidity for the beams. [15]
Figure 2:
3. Find the moment of resistance of a square beam cross-section if one of its diagonalis placed vertical. Assume the cross-sectional area is 2500 mm2 and the permissiblebending stress is 40 N /mm2. [15]
4. A compound cylinder comprises an inner tube of diameters 350 mm and 450 mm,and an outer tube of diameters 400 mm and 500 mm. determine the diametralinterference required so that the final maximum stress in the tube does not exceed180 MPa under an internal pressure of 55 MPa. Neglect the effects of longitudinalstresses. Assume E = 250 GPa. [15]
5. Direct stresses of 100 N/m2 (tensile) and 90 N/mm2 (compressive) exist on twoperpendicular planes at a certain point in a body. They are also accompanied byshear stresses on the planes. The greater principal stress at the point due to theseis 150 N/mm2,
(b) Find also the maximum shear stress at the point. [15]
6. A composite bar consists of a steel rod 3 m long and 25 mm diameter encased in acopper tube 25 mm internal diameter and 32 mm external diameter. A weight of10 kN is dropped from a height of 20 mm on to a collar fixed at the bottom end ofthe composite bar. Calculate the maximum instantaneous stresses induced in thetwo components. Assume E = 200 GN/m2 for steel and 100 GN/m2 for copper.
[15]
7. A pressurised cylinder of 450 mm internal diameter and 6 mm wall thickness reg-istered a pressure fall of 0.21 MPa when subjected to an axial tension of 470.0 kN.Determine the poisons ratio of the material. Assume E = 210 GPa for the cylinderand K = 2.9 GPa for the fluid. [15]
8. A prismatic beam of weight W, length L rests on two simple supports A and B,A being at one end. Find the position of B which gives the least value of themaximum bending moment. For this position find the reactions, the maximumbending moment and the point of contra flexure. [15]
II B.Tech I Semester Examinations,November 2010STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. A pressurized cylinder of 360 mm internal diameter and 3 mm wall thickness reg-istered a pressure of 0.15 MPa when subjected to an axial compression of 63 kN.Determine the poisons ratio of the material. Assume E = 150 GPa for the cylinderand K = 2.5 GPa for the fluid. [15]
2. Find the elongation of a bar, length L and cross-sectional area A, under the actionof its own weight. Assume the unit weight of the bar is w/unit length. [15]
3. (a) What are the advantages of compound cylinders? Explain analytically.
(b) What are the advantages and disadvantages of shell structures? [15]
4. A beam of I - section 300 mm deep and 200 mm wide, has equal flanges 20 mmthick and web 12 mm thick. It carries, at a section a shear force of 250 kN. Drawthe distribution of shear stress across the section and also calculate the total shearforce carried by the web. [15]
5. A simply supported beam of span 7 m carries a uniformly distributed load of 25kN/m run over the length of left half of its span, together with concentrated loadsof 30 kN, 75 kN and 50 kN situated at 1.0m, 2.0m and 3.5 m respectively fromright support. Draw the shear force and bending moment diagrams and find outthe magnitude and position of the maximum bending moment. [15]
6. A beam of T-section, flange 150 mm × 25 mm, width of the web 25 mm andoverall depth of the section 200 mm is simply supported over a span 4.5 m and isso arranged that the flange is uppermost. It carries a uniformly distributed load of40 kN /m over its entire span. Find the maximum tensile and compressive stresses.
[15]
7. Compute the maximum deflections and support rotations in the beams of the fol-lowing figure 7 using
(a) The methods of integration and
(b) The method of moment area. [15]
8. At a point in strained material the principal stresses are 60 N/mm2 and 0 N/mm2.Find the position of plane across which the resultant stress is most inclined to thenormal and determine the value of this stress. [15]
II B.Tech I Semester Examinations,November 2010STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. (a) State the assumptions made in the theory of pure bending.
(b) Derive the flexure formula from first principle. [15]
2. Determine the elongation of a conical bar, length L and diameter at base D, underthe action of its own weight, assume the density of the material is ρ. [15]
3. At a point a beam section there is a longitudinal bending stress of 120 N/mm2
tensile and a transverse shear stress of 50 N/mm2. Find the resultant stress on aplane inclined at 300 to the longitudinal axis. [15]
4. Design a cylinder of 800 mm diameter to sustain an internal pressure of 36 MPaassuming a permissible stress of 200 MPa and Poisson’s ratio of 0.20. [15]
5. (a) Determine the length of overhang of the beam shown in figure 5, such thatthe displacement at D is zero.
6. Draw the shear force and bending moment diagrams for a beam supported of span6 m loaded as shown in figure 6. Also find and show the magnitude of maximumbending moment. [15]
Figure 6
7. A beam has a cross-sectional area in the form of an isosceles triangle having thedimensions base 100 mm and height h 200 mm. The cross-section of the beam issubjected to a vertical shear force of 125 kN. Draw the variation of the shear stressdistribution across the section. [15]
8. A cylinder of 200 mm diameter and 25 mm thickness is subjected to an internalpressure of 63 MPa. Determine the stress distribution and compare with thincylinder theory. Find the change in the thickness of the cylinder for ν = 0.22 andE = 210 GPa. [15]
II B.Tech I Semester Examinations,November 2010STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. The volume of a hollow cylinder of 800 mm diameter, 1.4 m length and 10 mmthickness increases by 1245 ml when subjected to an internal pressure of 4.5 MPa.Determine the Poissons ratio of the material, if E = 190.0 GPa. [15]
2. (a) At a point the principal stresses are 140 N/mm2 and 75 N/mm2 both tensile.Find the normal and tangential stresses on a plane inclined at 600 to the axisof the major principal stress.
(b) The principal stresses at a certain point in strained material are 150 N/mm2
and 48 N/mm2 both tensile. Find the normal and tangential stresses on aplane inclined at 0 with the major principal plane. [15]
3. (a) Define Poission’s ratio.
(b) Determine the volumetric strain of a rectangular bar of length L, width b anddepth d subjected to an axial load P from first principle. [15]
4. A steel H - beam section shown in figure 4, thickness 20 mm, is subjected to a shearforce of 250 kN. Draw the shear stress distribution across the depth of the section.Also determine ratio of maximum shear stress to the mean shear stress.
Figure 4:
[15]
5. A beam of I - section 250 mm × 125 mm has flanges 12.5 mm thick and web 6.9mm thick. Compare its flexural strength with that of a beam of rectangular sectionof same weight, the depth being twice the width. [15]
6. The maximum allowable stress in a cylinder of 500 mm inner diameter and 100.0mm thickness is 12.6 MPa. Determine the maximum allowable internal and externalpressures on the cylinder, when applied separately. [15]
7. Draw the shear force and bending moment diagrams for a beam supported andloaded as shown in figure 7. Locate the salient points. [15]
Figure 7
8. Compute the maximum deflections and support rotations in the beams of the fol-lowing figure 8 using
II B.Tech I Semester Examinations,November 2010STRENGTH OF MATERIALS-I
Civil EngineeringTime: 3 hours Max Marks: 75
Answer any FIVE QuestionsAll Questions carry equal marks
? ? ? ? ?
1. A simply supported steel beam of span 6m has I-section 350 mm deep and 165 mmwide has flanges 9.8 mm thick and web 7.0 mm thick. If the maximum permissiblestress is 165 N/mm2, find the safe uniformly distributed load that the section cancarry. [15]
2. A circular beam of 150 mm diameter is subjected to a shear force of 25 kN. De-termine the maximum shear stress, average shear stress and the shear stress at adistance of 25 mm from neutral axis. [15]
3. Develop the equilibrium equation for spherical shells subjected to radial pressure.[15]
4. Draw the shear force and bending moment diagrams for a simply supported beamloaded as shown in figure 4. Also find and show the magnitude of maximum bendingmoment. [15]
Figure 4
5. (a) Determine the deflection profile of a simply supported beam of 8 m span withan overhang of 2.5 m at one end when subjected to a clockwise moment of100 kNm at 3 m from its left support. Assume EI = 20 MNm2.
(b) Determine the mid-span displacements and slopes at the supports in the beamsshown in figure 5 using the method of integration. Assume constant flexuralrigidity for the beams. [15]
6. At a certain point in a piece of elastic material there are normal stresses of 45N/mm2 tension and 30N/mm2 compression on two planes at right angles to oneanother, together with shearing stresses of 22.50 N/mm2 on the same planes. Ifthe loading on the material is increased so that the stresses reach values of Ktimes those given, find the maximum value of K if the maximum direct stressis not to exceed 120 N/mm2 and the maximum shearing stress is not to exceed75 N/mm2. [15]
7. A mild steel bar 25 mm in diameter and 500 mm long is encased in a brass tubehaving external diameter is 40 mm and internal diameter is 32 mm. the compositebar is heated through 500 C. Calculate the stresses induced in each metal. Thecoefficient of expansion for steel and brass are 1.08 × 10−5 and 16.5 × 10−6 perdegree centigrade respectively. E = 2.1 × 105 N/mm2 for steel and 1.0 × 105
N/mm2 for brass. [15]
8. A pressurized cylinder of 325 mm internal diameter and 4 mm wall thickness reg-istered a pressure of 0.18 MPa when subjected to an axial compression of 63 kN.Determine the poisons ratio of the material. Assume E = 150 GPa for the cylinderand K = 2.5 GPa for the fluid. [15]
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