A circular post, a rectangular post, and a post of cruciform cross section are each compressed by loads that produce a resultant force P acting at the edge of the cross section (see figure). P b 4 x: = b 4 Load P here - d-y The diameter of the circular post and the depths of the rectangular and cruciform posts are the same. (a) For what width b of the rectangular post will the maximum tensile stresses be the same in the circular and rectangular posts? (Use the following as necessary: d.) b = (b) For what width b of the cruciform post will the maximum tensile stresses be the same in the circular and cruciform posts? (Use the following as necessary: d.) b = (c) Under the conditions described in parts (a) and (b), which post has the largest compressive stress? O circular post O rectangular post O cruciform post

A circular post, a rectangular post, and a post of cruciform cross section are each compressed by loads that produce a resultant force P acting at the edge of the cross section (see figure). P b 4 x: = b 4 Load P here - d-y The diameter of the circular post and the depths of the rectangular and cruciform posts are the same. (a) For what width b of the rectangular post will the maximum tensile stresses be the same in the circular and rectangular posts? (Use the following as necessary: d.) b = (b) For what width b of the cruciform post will the maximum tensile stresses be the same in the circular and cruciform posts? (Use the following as necessary: d.) b = (c) Under the conditions described in parts (a) and (b), which post has the largest compressive stress? O circular post O rectangular post O cruciform post

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter8: Applications Of Plane Stress (pressure Vessels, Beams, And Combined Loadings)

Section: Chapter Questions

Problem 8.4.9P: A simple beam with a rectangular cross section (width, 3,5 inL; height, 12 in,) carries a...

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The 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.
A 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?
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."
-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/in
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.
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.
A pressurized cylindrical tank with flat ends is loaded by torques T and tensile forces P (sec figure), The tank has a radius of r = 125 mm and wall thickness t = 6.5 mm. The internal pressure p = 7.25 MPa and the torque T = 850 N m. (a) What is the maximum permissible value of the forces P if the allowable tensile stress in the wall of the cylinder is 160 MPa? (b) If forces P = 400 kN, what is the maximum acceptable internal pressure in the tank?
-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.
A circular steel rod of diameter d is subjected to a tensile force P = 3.5 kN (see figure). The allow able stresses in tension and shear are 118 MPa and 4S MPa, respectively. What is the minimum permissible diameter dminof the rod?
A solid circular pole is subjected to linearly varying distributed force with maximum intensity q0at the base and an axial compressive load P at the top (see figure). Find the required diameter d of the pole if the maximum allowable normal stress is 150 M Pa. Let q0= 6.5 kN/m, P = 70 kN, and L = 3 m.
A 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.
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.