Q4) While removing a wheel to change a tire, a driver applies forces P-120 N at the ends of two of the arms of a lug wrench (see figure). The wrench is made of steel with shear modulus of elasticity G=80 GPa. Each arm of the wrench is 20 cm long and has a solid circular cross section of diameter d = 2 cm. (a) Determine the maximum shear stress in the arm th turning the lug nut (arm A). 20 cm d-2 cm 20 cm P-120 N
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- Consider the preceding problem if the beam has width h = 15 mm, the aluminum strips have thickness t = 3 mm, the plastic segments have heights d = 40 mm and 3 tf = 120 mm, and the total height of the beam is h = 212 mm. Also, the moduli of elasticity are EA= 75 GPa and Ep=3 GPa, respectively. Determine the maximum stresses o., and o\, in the aluminum and plastic, respectively, due to a bending moment of 1.0 kN - m.A cylindrical pressure vessel having a radius r = 14 in. and wall thickness t = 0,5 in, is subjected to internal pressure p = 375 psi, In addition, a torque T = 90 kip-ft acts at each end of the cylinder (see figure), (a) Determine the maximum tensile stress ctniXand the maximum in-plane shear stress Tmjv in the wall of the cylinder. (b) If the allowable in-plane shear stress is 4.5 ksi, what is the maximum allowable torque T\ (c) If 7 = 150 kip-ft and allowable in-plane shear and allowable normal stresses are 4.5 ksi and 11.5 ksi, respectively, what is the minimum required wall thicknessA tubular bar with outside diameterd2= 4.0 in, is twisted by torques T = 70,0 kip-in. (see figure). Under the action of these torques, the maximum tensile stress in the bar is found to be 6400 psi. Determine the inside diameter rtf of the bar. If the bar has length L = 48.0 in. and is made of aluminum with shear modulus G = 4,0 × 106 psi, what is the angle of twist d (in degrees) between the ends of the bar? (c) Determine the maximum shear strain y (in radians)?
- The composite beam shown in the figure is simply supported and carries a total uniform load of 40 kN/m on a span length of 4.0 m. The beam is built of a southern pine wood member having cross-sectional dimensions of 150 mm × 250 mm and two brass plates of cross-sectional dimensions 30 mm × 150 mm. Determine the maximum stresses (7b and ctwin the brass and wood, respectively, if the moduli of elasticity are EB= % GPa and Ew= 14 GPa. (Disregard the weight of the beam.) Find the required thickness of the brass plates so that the plate and wood reach their allowable stress values of Eb= 70 MPa and t Ew= 8.5 MPa simultaneously under the maximum moment. What is the maximum moment?A thin-walled steel tube of rectangular cross section (see figure) has centerline dimensions b = 150 mm and h = 100 mm. The wall thickness t is constant and equal to 6.0 mm. Determine the shear stress in the tube due to a torque T = 1650 N · m. Determine the angle of twist (in degrees) if the length L of the tube is 1.2 m and the shear modulus G is 75 GPa.A wood beam reinforced by an aluminum channel section is shown in the figure. The beam has a cross section of dimensions 150 mm x 250 mm, and the channel has a uniform thickness of 6.5 mm. If the allowable stresses in the wood and aluminum are 8 M Pa and 38 M Pa, respectively, and if their moduli of elasticity are in the ratio 1 to 6, what is the maximum allowable bending moment for the beam?
- A plastic-lined steel pipe has the cross-sectional shape shown in the figure. The steel pipe has an outer diameter d1= 100 mm and an inner diameter d2= 94 mm. The plastic liner has an inner diameter d1= 82 mm. The modulus of elasticity of the steel is 75 times the modulus of the plastic. Determine the allowable bending moment Mallowif the allowable stress in the steel is 35 M Pa and in the plastic is 600 kPa. If pipe and liner diameters remain unchanged, what new value of allowable stress for the steel pipe will result in the steel pipe and plastic liner reaching their allowable stress values under the same maximum moment (i.e., a balanced design)? What is the new maximum moment?The cross section of a composite beam made of aluminum and steel is shown in the figure. The moduli of elasticity are TA= 75 GPa and Es= 200 GPa. Under the action of a bending moment that produces a maximum stress of 50 M Pa in the aluminum, what is the maximum stress xs in the steel? If the height of the beam remains at 120 mm and allowable stresses in steel and aluminum are defined as 94 M Pa and 40 M Pa, respectively, what heights h and h. arc required for aluminum and steel, respectively, so that both steel and aluminum reach their allowable stress values under the maximum moment?A circular aluminum tube subjected to pure torsion by torques T(sec figure) has an outer radius r2equal to 1.5 times the inner radius r1. (a) If the maximum shear strain in the tube is measured as 400 × 10-6 rad, what is the shear strain y1at the inner surface? (b) If the maximum a1lo-abk rate of twist is 0.125 °/m and the maximum shear strain is to be kept at 400 × 10-6 rad by adjusting the torque T, that is the minimum required outer radius ( r2)Min?
- A vertical pole of solid, circular cross section is twisted by horizontal forces P = 5kN acting at the ends of a rigid horizontal arm AB (see figure part a). The distance from the outside of the pole to the line of action of each force is c = 125 mm (sec figure part b) and the pole height L = 350 mm. (a) If the allowable shear stress in the pole is 30 MPa, what is the minimum required diameter dminof the pole? (b) What is the torsional stiffness of the pole (kN · m/rad)? Assume that G = 28 GPa. (c) If two translation al springs, each with stiffness k =2550 kN/m, are added at 2c/5 from A and B (see figure part c), repeat part (a) to find dmin. Hint: Consider the pole and pair of springs as "springs in parallel."A solid circular bar having diameter d is to be replaced by a rectangular tube having cross-sectional dimensions d × 2d to the median line of the cross section (see figure). Determine the required thickness tminof the tube so that the maximum shear stress in the tube will not exceed the maximum shear stress in the solid bar.A square steel tube of a length L = 20 ft and width b2= 10.0 in. is hoisted by a crane (see figure). The lube hangs from a pin of diameter d that is held by the cables at points A and B. The cross section is a hollow square with an inner dimension b1= 8.5 in. and outer dimension b2= 10,0 in. The allowable shear stress in the pin is 8,700 psi. and the allowable bearing stress between the pin and the tube is 13,000 psi. Determine the minimum diameter of the pin in order to support the weight of the tube. Note: Disregard the rounded corners of the tube when calculating its weight.