101 Solving Problems in Strength of Materials PROBLEM 1.

The bar supported by a pin at A and a cable B carries a load of 260 N at C neglecting the weight of the bar.

1.1. Which of the following gives the normal force on the bar segment on the left of a section which is

3 meters from A. (see figure) A. 44.22 B. 44.00 C. 43.45 D. 44.35 E. 46.00 1.2. Which of the following gives the shear force on the bar segment on the left of a section which is 3 meters from A. A. 9.42N B. 9.56 N C. 9.59N D.9.13 N E. 9.25 1.3 Which of the following gives the bending moment on the bar segment on the left of a section which is 3 meters from A. A 27.88N-m B. 28.01N-m C. 26.98 N-m D. 28.26 N-m E. 27.08

PROBLEM 2 .

A homogeneous 800kg bar AB is supported at either end by a cable as shown in fig p-105. calculate the smallest area of each cable if the stress is not to exceed 90Mpa in bronze and 120Mpa in steel.

4m bronze steel

10m 3m

A B

A) 30.4mm² B) 34.5 mm² C) 33.6 mm² D) 32.7mm² E) none of the above

PROBLEM 3.The homogeneous bar shown in fig. P-106 is supported by a smooth pin at C and cable that

runs from A to B around the smooth peg at D. Find the stress in the cable if its diameter is 0.6 in. and the bar weighs 6000lbs

A) 9602.7 psi B) 10,458.7 psi C) 10,450.8psi D) 93432 psi E) none of the above

PROBLEM 4A rod is composed of an aluminum section rigidly attached between steel and bronze sections

as shown in fig. P-107. axial loads are applied at the positions indicated. If P= 3000lb and the cross-sectional area of the rod is 0.5 in², determine the stress in each section.

A) 24000 psi,steel B) 25000psi steel C) 26000psi steel D)27000psi steel 24000 psi AL 24000psi Al 23000psi AL 25000psi AL 18000 psi bronze 23000psi bronze 18000psi bronze 19000psi bronze

PROBLEM 5

For the beam loaded see figure 5.1. Which of the following most nearly gives the vertical reaction at R1

A. P + 20 B. P + 21 C. P + 25 D. P + 34 E. P + 36 5.2. Which of the following most nearly gives the moment at B. A. P + 26 B. P + 25 C. P + 27 D. P + 23 E. P + 22 5.3 Which of the following most nearly gives the moment at E A. 20-2P B. 20 - P C. P + 20 D. P-22 E. P + 08 5.4 Which of the following most nearly gives the value of P in KN A. 8.75 KN B. 10.50 KN C. 15.20 KN D. 15.10 KN E. 15.98KN

Problem 5 figure

PROBLEM 6As in fig problem 6 , a hole is to be punched out of a plate having a shearing strength of 40 ksi. The compressive stress in the punch is limited to 50ksi. Compute the maximum thickness of the plate from which a hole 2.5 in. in diameter can be punched

Problem 6 figure:

A) .657 in B) .871in C) .781in D) .730in E) none of the above

PROBLEM 7 Two steel plates spliced to each other using a two inch-diameter bolts. The dimension of the steel plates is 100 mm x 25.10 mm, if the allowable stress for the steel plate is 80 MPa and the allowable shear stress for the bolts is 198 MPa. Compute the safe load P. A. 200 KN B. 200.66 KN C. 199.54 KN D. 200.80 KN

Problem 7 figure:

PROBLEM 8Find the smallest diameter bolt that can be used in the clevis in fig problem 8, if P=400kN. The

shearing strength for the bolt is 300 MPa

Problem 8 figure:

A) 28.11mm B) 29.13mm C)27.9mm D) 28.11mm E)none of the above

PROBLEM 9

A 200-mm-diameter pulley is prevented from rotating relatively to a 60-mm-diameter shaft by a 70-mm-long key, as shown in fig P-118. if a torque T=2.2KN-m is applied to the shaft , determine the width b if the allowable shearing stress in the key is 60Mpa.

A)19mm B) 20mm C) 18mm D) 21mm E) none of the above

PROBLEM 10

For the beam loaded (see figure problem 10)

10.1. Which of the following most nearly gives the vertical reaction at the roller supported in KN A. 13 KN B. 16 KN C. 27 KN D. 24 KN E. 33KN 10.2. Which of the following most nearly gives the maximum shear on the beam in KN A. 10 KN B. 15 KN C. 13 KN D. 17 KN E. 20KN 10.3 Which of the following most nearly gives the maximum bending moment on the beam in KN A. 13 KN B. 12 KN C. 8 KN D. 9.45 KN E. 10KN

Problem 10 figure

PROBLEM 11The wall thickness of a 4-ft-diameter spherical tank is 5/16 in. calculate the allowable internal

pressure if the stress is limited to 8000psi.

A) 205.5psi B) 203.5psi C) 211.6psi D) 208.3psi E) none of the above

PROBLEM 12Calculate the minimum wall thickness for a cylindrical vessel that is to carry a gas at a

pressure of 1400psi. The diameter of the vessel is 2ft, and the stress is limited to 12ksi.

A) 2 in B) 3 in C) 4 in D) 5 in E) none of the above

PROBLEM 13A cylindrical pressure vessel is fabricated from steel planting that a thickness of 20mm. The

diameter of the pressure vessel is 450mm and its length is 2.0m. Determine the maximum internal pressure that can be applied if the longitudinal stress is limited to 140 Mpa, and the circumferential stress is limited 60Mpa.

A) 5.33Mpa B) 24.89Mpa C) 27.28Mpa D) 10.57Mpa E) none of the above

PROBLEM 14A water tank, 22ft in diameter, is made from steel plates that are ½ in. thick. Find the maximum

height to which the tank may be filled if the circumferential stress is limited to 6000psi. the specific weight of water is 62.4 lb/ft³.

A) 50.6ft B) 45.7 ft C) 52.4ft D) 44.3ft E) none of the above

PROBLEM 15The strength of the longitudinal joint in figure problem 15, is 33 kips/ft. whereas for the girth

joint it is 16 kips/ft. calculate the maximum diameter of the cylindrical tank if the internal pressure is 150psi

Problem 15 figure

A) 36.7 in B) 37.6 in C) 35.6 in D) 36.5 in E) none of the above

PROBLEM 16At what angular velocity will the stress in a rotating steel ring equal 150 Mpa if its mean radius

is 220 mm? The density of steel is 7.85 mg/m³.

A) 728.3 rad/s B) 528.5 rad/s C) 628.3 rad/s D) 599.22 rad/s E) none of the above

PROBLEM 17The tank shown in figure Problem 17, is fabricated from 1/8-in. steel plate. Calculate the

maximum longitudinal and circumferential stress caused by an internal pressure of 125 psi.

A) 9119 psi B) 7177 psi C) 6566 psi D) 5566 psi E) none of the above

Figure problem 17

PROBLEM 18A steel rod having a cross-sectional area of 300 mm² and a length of 150m is suspended

vertically from one end. It supports a tensile load of 20kN at the lower end. If the unit mass of steel is 7850 kg/m³ and E= 200x10³MN/m² find the total elongation of the rod.

A) 56.5mm B) 52.3mm C) 54.3mm D) 55.5mm E)none of the above

PROBLEM 19 The rigid bar AB, attached to two vertical rods as shown in figure problem 19, is horizontal

before the load P is applied. Determine the vertical movement of P if its magnitude is 50KN.

A) 1.665 mm B) 1.784mm C) 1.879mm D) 1.982mm E) none of the above

PROBLEM 20A uniform concrete slab of total weight W is to be attached as shown in figure problem 20.. To

two rods whose lower ends are on the same level. Determine the ration of the areas of the rods so that the slab will remain level

A) 4.32 B) 3.45 C) 3.87 D) 4.36 E) none of the above

PROBLEM 21A steel rod is stretched between two rigid walls and carries a tensile load of 5000N at 20º C,

what is the minimum diameter of the rod? Assume = 11.7 цm/mºC and E= 200 Gpa

A) 12.5mm B) 11.5mm C) 13.2mm D) 14.3mm E) none of the above

PROBLEM 22 A steel shaft 3ft long that has a diameter of 4 in. is subjected to a torque of 15 kip-ft.

determine the maximum shearing stress and the angle of twist. Use G= 12x10^6 psi.

A)14.3 ksi,1.23º B)15.3ksi, 2.31º C)13. 3ksi,1.53º D)14.9ksi, 2.2ºE) none of the above

Figure problem 19

Figure problem 20

PROBLEM 23A steel marine propeller shaft 14in. in diameter and 18ft long is used to transmit 5000hp at 189

rpm. If G = 12x10^6 psi, determine the maximum shearing stress

A) 4054 psi B) 3095 psi C) 3298 psi D) 3132 psi E) none of the above

PROBLEM 24A solid steel shaft 5m long is stressed to 80 Mpa when twisted through 4º. Using G= 83Gpa,

compute the shaft diameter. What power can be transmitted by the shaft at 20Hz

A) 4.2 MW B) 3.2 MW C) 5.2 MW D) 6.2MW E) none of the above

PROBLEM 25A 2-in-diameter steel shaft rotates at 240 rpm. If the shearing stress is limited to 12ksi,

determine the maximum horsepower that can be transmitted

A) 67.2 hp B) 75.4 hp C) 81.4 hp D) 71.8 hp E) none of the above

PROBLEM 26A flexible shaft consist of a 0.20 in-diameter steel wire enclosed in a stationary tube that fits

closely enough to impose a frictional torque of 0.50 lb-in/in. determine the maximum length of the shaft if the shearing stress is not to exceed 20 ksi. What will be the angular deformation of one end relative to the other end? G= 12x10^6 psi.

A) 59.9º B) 69.6º C) 49.4º D) 79.7º E) none of the above

PROBLEM 27A flanged bolt coupling consists of ten steel 20-mm diameter bolts spaced evenly around a bolt

circle 400 mm in diameter. Determine the torque capacity of the coupling if the allowable shearing stress in the bolts is 40Mpa.

A) 25.13 KN-m B) 26.34KN-m C) 27.43KN-m D) 23.4KN-m E) none of the above

PROBLEM 28A flanged bolt coupling consist of ten steel ½ in- diameter bolts spaced evenly around a bolt

circle 14in in diameter. Determine the torque capacity of the coupling if the allowable shearing stress in the bolts is 6000 psi.

A) 4313 ft-lb B) 6573 ft-lb C) 5686 ft-lb D) 6872 ft-lb E) none of the above

PROBLEM 29A uniform concrete slab of mass M is to be attached (figure problem 29 ) a two rods whose

lower ends are initially at the same level.

29.1. Which of the following gives the area of aluminum bar so that the slab will remain level after it is attached to the rods. A. 2571mm2 B. 2574mm2 C. 2579mm2 D. 2576mm2 E. 28576mm2

29.2. Which of the following gives the stress in the steel rod if M = 18000 kg. A. 235.44 MPa B. 235.47 MPa C. 235.54 MPa D. 335.44 MPa E. 345MPa

29.3 Which of the following gives the stress in the aluminum rod if M = 18000 kg. A. 41.20 MPa B. 31.20Pa C. 41.27 MPa D. 51.20MPa E. 53.00MPa

PROBLEM 30Determine the maximum shearing stress and elongation in a bronze helical spring composed

of 20 turns of 1.0-in-diameter wire on mean radius of 4 in. when the spring is supporting a load of 500 lb. Use eq.(3-10) and G= 6x10^6

A) 6.83 in B) 9.43 in C) 7.54 in D) 5.76 in E) none of the above

PROBLEM 31Determine the length of the shortest 2 mm diameter bronze wire, which be twisted through two complete turns without exceeding a stress of 70Mpa. Use G = 35 GPa. A. 6.28 m B. 5.23 m C. 6.89m D. 8.56m E. 9.00m

PROBLEM 32A force of 10 Newton is applied to one end of a 10 inches diameter circular rod. Calculate the

stress. A. 0.20Kpa B. 0.05 KPa C. O.10 KPa D. 0.15 Kpa E. None

PROBLEM 33

A steel bar 50 mm in diameter and 2m long is surrounded by a shell of cast iron 5m thick. Compute the load that will compress the bar a total of 1mm in the length of 2m. Use Esteel = 200 GPa and Ecastiron =100GPa. A. 200 KN B. 240 KN C. 280 KN D. 320 KN E. none

PROBLEM 34What modulus of elasticity in tension is required to obtain a unit deformation of 0.00105 m/m from a load producing a unit tensile stress of 44,000 psi?

A. 42.300 x106 psi B. 41.202 x106 psi C. 43.101 x 106 psi

D. 41.905 x106 psi E. None

PROBLEM 35A hollow shaft has an inner diameter of 0.035 m and outer diameter of 0.06 m. Determine the

polar moment of inertia of the hollow shaft? A. 1.512 x 10-6m4 B. 1.112 x 10-6m4 C. 1.325 x 10-6m4 D. 1.125 x 10-6m4 E. 1.425 x 10-

6m4

Figure problem 29

PROBLEM 36 Determine the maximum shearing stress in a helical steel spring composed of 20 turns of 20 mm diameter wire on mean radius of 80 mm when the spring is supporting a load of 20 kN?

A. 529 Gpa B. 370 Gpa C. 25 Kpa D. 121 MPa

PROBLEM 37 The beam show in the figure problem 37, is 5-inchs wide and 10 inches deep. What is the maximum bending stress?

Figure problem 37:

B. 7721.0 psi B. 3420.9 psi C. 2888 psi D. 5500.3 psi

PROBLEM 38A 19-foot beam 10-inch wide and 20 inches high supports 1500 lb/ft on two supports 14 feet apart. The right end of the beam extends 2 feet past the support. What is the shearing stress midway between supports?

A. 1.0 psi B. 10.0 psi C. 67 psi D. 2.0 psi

PROBLEM 39For the bean shown in figure problem 39, draw the shear and moment diagran. What is the maximum moment?

A 15,000 B. 17,000 C. 1 2,000 D. 16,000

PROBLEM 40.A 2.5 inch diameter shaft s 2 ft. Long. Its maximum shear stress is 10,000 psi. What is the angular deflection in degree?

A. 0.96 B. 0.45 C. 0.78 D. 0.56

PROBLEM 41. A solid shaft 2.0 m long is transmitting 27 kN-m torque. If the shear modulus of the shaft material is 85 GPa and allowable shearing stress is 70 Mpa, determine the angle of twist between the two ends of the shaft.

A. 1.52o B. 1.02o C. 1.44o D. 1.32o

300 lb/ft

2000 lb

5ft 7ft 7ft

N.A. 10 inch

5 inch

700 lb/ft

3000 lbs5000 lbs

3ft 4ft 4ft 8ft

PROBLEM 42. A 14 ft simple beam uniformly loaded with 200 lbs per foot over its entire length. If the beam is 3.625 in wide and 7.625 in deep, what is the maximum bending stress?.

B. 7974 psi B. 8205 psi C. 6332 psi D. 1674 psi

PROBLEM 43. If the ultimate shear strength of a steel plate is 42,0000 lb/in2, what force is necessary to punch 0.625 in thick plate? A. 63,000 lbs B. 68,000 lbs C.61,800 lbs D. 66,800 lbs

PROBLEM 44. What force P is required to punch a ½ hole on a 3/8 in thick plate if the ultimate shear strength on the plate is 42,00 psi? A. 24,940 lbs B. 24,960 lbs C.24,620 lbs D. 24,740 lbs

PROBLEM 45.What modulus of elasticity in tension is required to obtain a unit deformation of 0.00105 m/m from a load producing a unit tensile stress of 44,000 psi? A. 42.300 x106 psi B. 41.202 x106 psi C. 43.101 x 106 psi D. 41.905 x106 psi

PROBLEM 46. A hollow shaft has an inner diameter of 0.035 m and outer diameter of 0.06 m. Compute for the torque if the shear stress is not to exceed 120 MPa in N-m A. 4500 B. 4100 C. 4300 D. 4150

PROBLEM 47. A force of 10 Newton is applied to one end of a 10 inches diameter circular rod. Calculate the stress. A. 0.20Kpa B. 0.05 KPa C. O.10 KPa D. 0.15 Kpa

PROBLEM 48.A steel bar 50 mm in diameter and 2m long is surrounded by a shell of cast iron 5m thick. Compute the load that will compress the bar a total of 1mm in the length of 2m. Use Esteel = 200 GPa and Ecastiron =100GPa.

A. 200 KN B. 240 KN C. 280 KN D. 320 KN

PROBLEM 49-51 The mass of the homogeneous bar AB (see figure problem 49-51 ) is 2000 kg. The bar is supported by a pin at B and a vertical surface at A.

49. Compute the vertical reaction at B. A. 19,429 N B. 19,620 N C. 19,560 N D. 19,344 N

50 Compute the horizontal reaction at B. A. 7357.5 N B. 7344.5 N C. 7455.4 N D. 7356.7 N

51 Determine the diameter of the smallest pin which can be used at B if its shear stress is limited to 60 MPa. A. 14.9mm B. 13.9 mm C. 14.34mm D. 14.89mm

Figure problem 49 - 51

PROBLEM 52 A 2.5 in diameter by 2 in long journal bear ing is to carry a 5500 lb load at 3600 rpm using SAE 40 lube oil at 200°F through a single hole at 25 psi. Compute the bearing pressure. A. 1100 psi B. 900 psi C. 1000 psi D. 950 spi

PROBLEM 53For the beam loaded (see figure problem 53), determine the maximum moment A. 512.4 KN-m B. 657.9 KN-m C. 559.7 KN-m D. 472.3 KN-m

Figure Problem 53

PROBLEM 54-55Three axle loads of 30 KN, 40 KN and 50 KN respectively and separated by 2 m between each load, roll as a unit cross a 12-m span. Determine the maximum moment and maximum shear.

54 Which of the following most nearly gives the maximum moment A. 280 KN-m B. 255 KN-m C. 313 KN-m D. 217 KN-m

55 Which of the following most nearly gives the maximum shear A. 71.13 KN B. 71.65 KN C. 71.80 KN D. 79.45 KN

PROBLEM 56Determine the outside diameter of a hollow steel tube that will carry a tensile load of 500KN at a stress of 140 MPa. Assume the wall thickness to be one-tenth of the outside diameter A. 123mm B. 113mm C. 103 mm D. 93mm

PROBLEM 57A beam with S 380 x 74 section is simply supported at the ends. It is supported a central concentrated load of 40 KN and a uniformly distributed load of 15 KN/m over its entire length, including the weight of the beam. Determine the maximum length if the flexural stress is not to exceed 140 MPa. S for the section is 1060 x 103 mm3 A. 6.62m B. 6.63m C. 6.60m D. 6.37m

PROBLEM 58-60The beam has a shear diagram shown in the figure see .(shear units in Kilo-Newton)

58. Which of the following most nearly gives the maximum positive bending moment in kN-m. A. 10 kN-m B. 30 kN-m C. 20-kN-m D. 40 kN-m

59. Which of the following most nearly gives the maximum negative bending moment in kN-m. A. 15 kN-m B. 43 kN-m C. 25-kN-m D. 36 kN-m

60. Which of the following most nearly gives the location of the infection point from the left support, in m. A. 3.2m B. 3.6m C. 4.2m D. 4.6m

Figure 2

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5

35

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