MCQ in Strength of Materials Part 3 | ECE Board Exam

This is the Multiple Choice Questions Part 3 of the Series in Strength of Materials as one of the General Engineering and Applied Sciences (GEAS) topics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize yourself with each and every question compiled here taken from various sources including past Board Questions in General Engineering and Applied Sciences (GEAS), Strength of Materials Books, Journals, and other Strength of Materials References.

Continue Practice Exam Test Questions Part 3 of the Series

⇐ MCQ in Strength of Materials Part 2 | ECE Board Exam

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101. Two plates are being pulled in opposite directions with a load of 20 kN. If the plates are secured by two bolts 75 mm in diameter, what is the shearing stress applied to each bolt?

A. 4.23 MPa

B. 3.21 MPa

C. 2.26 MPa

D. 1.28 MPa

102. Three plates, secured by a 60 mm bolt, are being pulled in opposite directions alternately. What pulling force is needed to shear off the bolt if it can withstand a stress of up to 175 MPa?

A. 434 kN

B. 242 kN

C. 495 kN

D. 272 kN

103. What force is required to punch off a 5 mm hole out of a 4 mm thick plate if the ultimate punching stress is 200 MPa?

A. 15.53 kN

B. 17.45 kN

C. 14.43 kN

D. 12.57 kN

104. A hole is to be punched out of a plate having an ultimate shearing stress of 300 MPa. If the compressive stress in the punch is limited to 400 MPa, determine the maximum thickness of plate from which a hole, 100 mm in diameter can be punched.

A. 33.3 mm

B. 17.9 mm

C. 13.4 mm

D. 26.9 mm

105. A cylindrical vessel with wall diameter of 15 mm containing gas holds pressure of 30 MPa. If the thickness is 10% of the inner diameter, what is the longitudinal stress?

A. 150 MPa

B. 125 MPa

C. 100 MPa

D. 75 MPa

106. What is the tangential stress in question 105?

A. 150 MPa

B. 125 MPa

C. 100 MPa

D. 75 MPa

107. If the tensile stress of a spherical vessel is limited to 17 MPa, what is the minimum thickness allowed if its inner radius is 7 mm containing gas with 20 N/mm2 of pressure?

A. 2.06 mm

B. 4.12 mm

C. 6.24 mm

D. 8.75 mm

108. What is the bearing stress if a 15 kN force is applied to plates 9 mm thick secured by a bolt 8 mm in diameter?

A. 453.32 MPa

B. 321.43 MPa

C. 431.43 MPa

D. 208.33 MPa

109. What is the elongation if a steel bar 7 m long is subjected to a temperature change of 17°C? Use α = 11.7 x 10^-6 / C^o.

A. 1.34 mm

B. 13.44 mm

C. 134.44 mm

D. 1.34 m

110. By how much will a 15 m steel rod with diameter of 3 mm elongate if it is subjected to a tensile load of 26 kN. Use E=200 GPa

A. 293.34 mm

B. 67.34 mm

C. 275.87 mm

D. 69.34 mm

111. At temperature of 25°C, a 17 m rod 8 mm in diameter is subjected to a tensile load of 24 kN. At what temperature without the load will the bar have the same elongation? Use α = 13.8 x 10^-6 / C° and E = 180 GPa.

A. 115°C

B. 217°C

C. 245°C

D. 287°C

112. A cylindrical bar 75 m long is attached to the ceiling atone end. At what new length could be expected if it has a unit mass of 5000 kg/m³? Use E = 750 MPa.

A. 75.023 m

B. 75.104 m

C. 75.184 m

D. 75.245 m

113. A 7 mm bar 9 m long is attached to the ceiling at one end. If a weight of 40 kN is hung on its lower end, what is the total elongation? Use E = 200 GPa and unit mass of kg/m³.

A. 46.78 mm

B. 45.34 mm

C. 48.33 mm

D. 52.23 mm

114. A steel wire 10 m long, hanging vertically supports a tensile load of 2000 N. Neglecting the weight of the wire, determine the required diameter if the stress is not to exceed 140 MPa and the total elongation is not to exceed 5 mm. Assume E = 200 GPa.

A. 4.26 mm

B. 3.12 mm

C. 5.05 mm

D. 2.46 mm

115. A steel rod having a cross-sectional area of 300 mm² and length of 150 m is suspended vertically from one end. It supports a load of 13 kN at the lower end. If the unit mass of steel is 5120 kg/m³ and E=200 GPa, find the total elongation of the rod.

A. 33.45 mm

B. 54.33 mm

C. 53.44 mm

D. 35.33 mm

116. What is the torsion on a solid cylindrical shaft whose diameter is 6 mm subjected to a rotational force of 27 N-m?

A. 434.31 MPa

B. 542.46 MPa

C. 255.44 MPa

D. 636.62 MPa

117. What is the maximum torque allowed if a 12 mm shaft is allowed torsion of up to 40 MPa only?

A. 13.57 N-m

B. 15.34 N-m

C. 18.34 N-m

D. 23.43 N-m

118. How many degrees of rotational deformation would occur on an 8 m cylindrical bar 8 mm in radius if it subjected to torque of 95 N-m?

A. 56.34°

B. 35.62°

C. 92.32°

D. 43.53°

119. What is the torque if the power transmitted by a shaft rotating at 30 rev/s is 1 MW?

A. 8.342 kN-m

B. 3.532 kN-m

C. 7.453 kN-m

D. 5.305 kN-m

120. A cylindrical solid shaft 7 mm in diameter is rotating at 18 rev/s. What is the maximum allowable power transmitted if the stress should not exceed 380 MPa?

A. 3.43 kW

B. 5.23 kW

C. 1.53 kW

D. 2.89 kW

121. Determine the length of the shortest 2-mm diameter bronze wire which can be twisted through two complete turns without exceeding a shearing stress of 343 MPa. Use G = 35 GPa.

A. 6280 mm

B. 3420 mm

C. 1280 mm

D. 1658 mm

122. A solid steel shaft 5 m long is stressed to 60 Mpa when twisted through 4o. Using G=83 GPa, compute the power that can be transmitted by the shaft at 20 rev/s.

A. 1.21 MW

B. 1.67 MW

C. 3.21 MW

D. 1.26 MW

123. A helical spring with mean radius of 40 mm has wire diameter of 2.7 mm. What is the shearing stress if there is a 22 N load? Use the approximate formula.

A. 325.32 MPa

B. 231.54 MPa

C. 432.43 MPa

D. 154.67 MPa

124. Solve question 123 using the exact formula.

A. 238.29 MPa

B. 431.32 MPa

C. 365.35 MPa

D. 153.64 MPa

125. By how much will a spring with 9 turns elongate if it supports a weight of 400 N? The wire diameter is 6 mm and the mean radius is 28 mm. Use G=150 GPa.

A. 64.35 mm

B. 42.43 mm

C. 26.02 mm

D. 16.65 mm

126. A helical spring is made by wrapping steel wire 20 mm in diameter around a forming cylinder 150 mm in diameter. Compute number of turns required to permit an elongation of 132 mm without exceeding a shearing stress of 184.8 MPa. Use G = 83 GPa.

A. 15.43 turns

B. 13.83 turns

C. 18.24 turns

D. 12.36 turns

127. Determine the maximum shearing stress in a helical steel spring composed of 20 turns of 20-mm diameter wire on a mean radius of 80 mm when the spring is supporting a load of 2 kN. Use the exact formula.

A. 120.6 MPa

B. 117.9 MPa

C. 132.4 MPa

D. 126.9 MPa

128. A force of 10 N is applied to one end of a 10 inches diameter circular rod. Calculate the stress.

A. 0.20 kPa

B. 0.05 kPa

C. 0.10 kPa

D. 0.15 kPa

129. What force is required to punch a 20-mm diameter hole through a 10-mm thick plate? The ultimate strength of the plate material is 450 MPa.

A. 241 kN

B. 283 kN

C. 386 kN

D. 252 kN

130. A steel pipe 1.5m in diameter is required to carry an internal pressure of 750 kPa. If the allowable tensile stress of steel is 140 MPa, determine the required thickness of the pipe in mm.

A. 4.56

B. 5.12

C. 4.25

D. 4.01

131. A spherical pressure vessel 400-mm in diameter has a uniform thickness of 6 mm. The vessel contains gas under a pressure of 8,000 kPa. If the ultimate stress of the material is 420 MPa, what is the factor of safety with respect to tensile failure?

A. 3.15

B. 3.55

C. 2.15

D. 2.55

132. A metal specimen 36-mm in diameter has a length of 360 mm and a force of 300 kN elongates the length bar to 1.20-mm. What is the modulus of elasticity?

A. 88.419 GPa

B. 92.564 GPa

C. 92.658 GPa

D. 95.635 GPa

133. During a stress-strain test, the unit deformation at a stress of 35 MPa was observed to be 167 x 10-6 m/m and at a stress of 140 MPa it was 667 x 10-6 m/m. If the proportional limit was 200 MPa, what is the modulus of elasticity? What is the strain corresponding to stress of 80 MPa?

A. E = 210,000 MPa; ε = 381 x 10^-4  m/m

B. E = 200,000 MPa; ε = 318 x 10^-6  m/m

C. E = 211,000 MPa; ε = 318 x 10^-4  m/m

D. E = 210,000 MPa; ε = 381 x 10^-6  m/m

134. An axial load of 100 kN is applied to a flat bar 20 mm thick, tapering in width from 120 mm to 40 mm in a length of 10 m. Assuming E = 200 GPa, determine the total elongation of the bar.

A. 3.43 mm

B. 2.125 mm

C. 4.33 mm

D. 1.985 mm

135. Steel bar having a rectangular cross-section 15mm, 20mm and 150m long is suspended vertically from one end. The steel has a unit mass of 7850 kg/m3 and a modulus of elasticity E of 200 GPa. If a loaf of 20 kN is suspended at the other end of the rod, determine the total elongation of the rod.

A. 43.5 mm

B. 54.3 mm

C. 35.4 mm

D. 45.3 mm

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

A. 200 kN

B. 240 kN

C. 280 kN

D. 320 kN

137. A 20-mm diameter steel rod, 250 mm long is subjected to a tensile force of 75 kN. If the Poisson’s ratio µ  is 0.30, determine the lateral strain of the rod. Use E = 200 GPa.

A. εy = 3.581 x 10^-4 mm/mm

B. εy = -3.581 x 10^-4 mm/mm

C. εy = -2.467 x 10^-4 mm/mm

D. εy = 2.467 x 10^-4 mm/mm

138. A solid aluminum shaft of 100-mm diameter fits concentrically in a hollow steel tube. Determine the minimum internal diameter of the steel tube so that no contact pressure exists when the aluminum shaft carries an axial compressive load of 600 kN. Assume Poisson’s ratio µ = 1/3 and the modulus of elasticity of aluminum E be 70 GPa.

A. 100.0364 mm

B. 100.0312 mm

C. 100.0303 mm

D. 100.0414 mm

139. The maximum allowable torque, in kN-m, for a 50-mm diameter steel shaft when the allowable shearing stress is 81.5 MPa is:

A. 3.0

B. 1.0

C. 4.0

D. 2.0

140. The rotation or twist in degrees of a shaft, 800 mm long subjected to a torque of 80 N-m, 20 mm in diameter and shear modulus G of 80,000 MPa is:

A. 3.03

B. 4.04

C. 2.92

D. 1.81

141. Compute the value of the shear modulus G of steel whose modulus of elasticity E is 200 GPa and Poisson’s ratio is µ is 0.30.

A. 72,456 MPa

B. 76,923 MPa

C. 79,698 MPa

D. 82,400 MPa

142. Determine the length of the shortest 2-mm diameter bronze wire, which can be twisted through two complete turns without exceeding a stress of 70 MPa. Use G = 35 GPa.

A. 6.28 m

B. 5.23 m

C. 6.89 m

D. 8.56 m

143. A hollow steel shaft 2540 mm long must transmit torque of 34 kN-m. The total angle of twist must not exceed 3 degrees. The maximum shearing stress must not exceed 110 MPa. Find the inside diameter and the outside diameter of the shaft the meets these conditions. Use G = 83 GPa.

A. D = 129 mm; d = 92 mm

B. D = 125 mm; d = 65 mm

C. D = 132 mm; d = 100 mm

D. D = 112 mm; d = 85 mm

144. Determine the maximum shearing stress in a helical steel spring composed of 20 turns of 20-mm diameter wire on a mean radius of 80 mm when the spring is supporting a load of 2 kN.

A. 110.6 MPa

B. 101.1 MPa

C. 120.6 MPa

D. 136.5 MPa

145. A load P is supported by two springs arranged in series. The upper spring has 20 turns of 29-mm diameter wire on a mean diameter of 150 mm. The lower spring consist of 15 turns of 10-mm diameter wire on a mean diameter of 130 mm. Determine the value of P that will cause a total deflection of 80 mm. Assume G = 80 GPa for both spring.

A. 223.3 N

B. 228.8 N

C. 214.8 N

D. 278.4 N

146. A 10-meter long simply supported beam carries a uniform load of 8 kN/m for 6 meters from the left support and a concentrated load of 15 kN 2 meters from the right support. Determine the maximum shear and moment.

A. Vmax = 33.2 kN; Mmax = 85.92 KN-m

B. Vmax = 31.3 kN; Mmax = 81.74 KN-m

C. Vmax = 36.6 kN; Mmax = 83.72 KN-m

D. Vmax = 41.8 kN; Mmax = 92.23 KN-m

147. A simple beam, 10 m long carries a concentrated load of 500 kN at the midspan. What is the maximum moment of the beam?

A. 1250 kN-m

B. 1050 kN-m

C. 1520 kN-m

D. 1510 kN-m

148. A small square 5cm by 5cm is cut out of one corner of a rectangular cardboard 20cm wide by 30cm long. How far, in cm from the uncut longer side, is the centroid of the remaining area?

A. 9.56

B. 9.35

C. 9.48

D. 9.67

149. What is the inertia of a bowling ball (mass = 0.5 kg) of radius 15 cm rotating at an angular speed of 10 rpm for 6 seconds?

A. 0.0045 kg-m²

B. 0.001 kg-m²

C. 0.005 kg-m²

D. 0.002 kg-m²

150. What is the moment of inertia of a cylinder of radius 5 m and mass of 5 kg?

A. 62.5 kg-m²

B. 80 kg-m²

C. 72.5 kg-m²

D. 120 kg-m²

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