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A moveable steel stand supports an automobile engine weighing W = 750 lb, as shown in the figure part a. The stand is constructed of 2.5 in. x 2.5 in. x 1/8 in.-thick steel tubing. Once in position, the stand is restrained by pin supports at B and C. Of interest are stresses at point A at the base of the vertical post; point A has coordinates (x = 1.25, y = 0, z = 1.25) in inches. Neglect the weight of the stand.
(a) Initially, the engine weight acts in the — z direction through point Q, which has coordinates (24, 0, 1.25) inches. Find the maximum tensile, compressive, and shear stresses at point A.
(b) Repeat part (a) assuming now that, during repair, the engine is rotated about its own longitudinal axis (which is parallel to the x axis) so that Warts through Q [with coordinates (24, 6, 1.25) in inches] and force F = 200 lb is applied parallel to the y axis at distance d = 30 in
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Chapter 8 Solutions
Mechanics of Materials (MindTap Course List)
- • - 3 A rectangular plate in biaxial stress (see figure) is subjected to normal stresses u = 67 MPa (tension) and s = -23 MPa (compression). The plate has dimensions 400 X 550 X 20 mm and is made of steel with E = 200 GPa and v = 0.30. (a) Determine the maximum in-plane shear strain ?max in the plate. (b) Determine the change ?t in the thickness of the plate. (c) Determine the change ?t in the volume of the plate.arrow_forwardThe upper deck ala foothill stadium is supported by braces, each of which transfer a load P = 160 kips to the base of a column (see figure part a). A cap plate at the bottom of the brace distributes the load P to four flange pates (:1 = I in)t hrough a pin(d, = 2 in.) to two gusset plates t8 = l.5 in.) (see figure parts b and c). Determine the following quantities. (a) The average shear stress i in the pin. (b) The average bearing stress between the flange plates and the pin and also between the gusset plates and the pin Disregard friction between the plates. Determine the following quantities. (a) The average shear stress i in the pin. (b) The average bearing stress between the flange plates and the pin and also between the gusset plates and the pin (7j )L Disregard friction between the plates.arrow_forwardA 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.arrow_forward
- The flat bars shown in parts a and b of the figure are subjected to tensile forces P = 2.5 kN. Each bar has thickness t = 5.0 mm. (a) For the bar with a circular hole, determine the maximum stresses for hole diameters d = 12 mm and d = 20 mm il" the width h = 60 mm. (b) For the stepped bar with shoulder fillets, determine the maximum stresses Tor fillet radii R = 6 mm and R = 10 mm if the bar widths are h = 60 mm and c = 40 mm.arrow_forwardA standard brick (dimensions 8 in. × 4 in. × 2.5 in ) is compressed lengthwise by a force P. as shown in the figure, If the ultimate shear stress for brick is 1200 psi and the ultimate compressive stress is 3600 psi. what force Pmax is required to break the brick?arrow_forwardA plastic bar of rectangular cross section (ft = 1.5 in. and h = 3 in.) fits snugly between rigid supporls at room temperature (68oF) but with no initial stress (see Figure). When the temperature of the bar is raised to 160oF, the compressive stress on an inclined plane pq at mid-span becomes 1700 psi. (a) What is the shear stress on plane pq? (Assume a = 60 × 10-6/*t and E = 450 × 103psi.) (b) Draw a stress element oriented to plane pq and show the stresses acting on all laces of this element. (c) If the allowable normal stress is 3400 psi and the allowable shear stress is 1650 psi. what is the maximum load P (in the positive x direction), which can be added at the quarter point (in addition to thermal effects given) without exceeding allowable stress values in the bar?arrow_forward
- A copper bar with a rectangular cross section is held without stress between rigid supports (see figure). Subsequently, the temperature of the bar is raised 50°C (a) Determine the stresses on all faces of the elements A and B, and show these stresses on sketches of the elements. (Assume = 17.5 × 10-6/? and E = 120 GPa ) (b) If the shear stress at B is known to be 48 MPa at some inclination 8, find anglearrow_forward-11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0 kip-in. acting in the directions shown in the figure. Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.arrow_forward-21 Plastic bar AB of rectangular cross section (6 = 0.75 in. and h = 1.5 in.) and length L = 2 Ft is Fixed at A and has a spring support (Ar = 18 kips/in.) at C (see figure). Initially, the bar and spring have no stress. When the temperature of the bar is raised hy foot. the compressive stress on an inclined plane pq at Lq = 1.5 Ft becomes 950 psi. Assume the spring is massless and is unaffected by the temperature change. Let a = 55 × l0-6p and E = 400 ksi. (a) What is the shear stresst9 on plane pq? What is angle 07 =1 Draw a stress element oriented to plane pq, and show the stresses acting on all laces of this element. (c) If the allowable normal stress is ± 1000 psi and the allowable shear stress is ±560 psi, what is the maximum permissible value of spring constant k if the allowable stress values in the bar are not to be exceeded? (d) What is the maximum permissible length L of the bar if the allowable stress values in the bar are not be exceeded? (Assume £ = IB kips/in.) (e) What is the maximum permissible temperature increase (A7") in the bar if the allowable stress values in the bar are not to be exceeded? (Assume L = 2 ft and k = L& kips/inarrow_forward
- The flat bars shown in parts a and b of the figure are subjected to tensile forces P = 3.0 kips. Each bar a has thickness t = 0.25 in. (a) For the bar with a circular hole, determine the maximum stresses for hole diameters d = 1 in. and d = 2 in. if the width b = 6.0 in. (b) For the stepped bar with shoulder fillets, determine the maximum stresses for fillet radii R = 0.25 in. and R = 0.5 in. if the bar widths are b = 4.0 in. and c = 2.5 in.arrow_forwardA copper bar of rectangular cross section (b = 18 mm and k = 40 mm) is held snugly (but without any initial stress) between rigid supports (see figure). The allowable stresses on the inclined plane pq at mid-span, for which ?? = 55°. are specified as 60 MPa in compression and 30 MPa in shear. (a) What is the maximum permissible temperature rise AT if the allowable stresses on plane pq are not to be exceeded? (Assume a = 17 × 10-6/oC and E = 120 GPa.) (b) If the temperature increases by the maximum permissible amount, what are the stresses on plane pq? (c) If the temperature rises AT = 2SoC how far to the right of end A (distance BL, which is expressed as a fraction of length L) can load P = 15 kN be applied without exceeding allowable stress values in the bar? Assume that a =75 MPa and t = 35 MPa.arrow_forwardA hollow, circular, cast-iron pipe (Ec =12,000 ksi) supports a brass rod (Ec= 14,000 ksi} and weight W — 2 kips, as shown. The outside diameter of the pipe is dc= 6 in. (a) If the allowable compressive stress in the pipe is S00O psi and the allowable shortening of the pipe is 0.02 in., what is the minimum required wall thickness trmm? (Include the weights of the rod and steel cap in your calculations.) (b) What is the elongation of the brass rod Srdue to both load Wand its own weight? (c) What is the minimum required clearance h?arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning