ES230 Strength of Materials Exam 6 - Compilation Prof. Kurtz, ES230 STRENGTH OF MATERIALS Exam 6 Wednesday, April 26, 2017, 7pm

Given Formulae Bending M/EI = 1/ = -y/ =My/I = E Beam Shear Stress = VQ/It q = VQ/I q = F/s Torsion I = ( /4)r 4 for a solid, circular shape of radius r Pressure Vessels hoop = Pr/t long = Pr/2t ES230 STRENGTH OF MATERIALS Exam 6 Wednesday, April 26, 2017, 7pm = Tc/J = TL/GJ Power P = T where T is torque and is angular frequency (rad/s) 1hp = 550 ft-lb/s 1Watt = 1 N-m/s J = ( /2)c 4 for a solid, circular shape of radius 1. (10 points). Two 2 x 4 boards are glued together and act as a cantilever beam over a span of 20 inches, subjected to an unknown point load P. It is known that the normal bending stresses at the extreme fibers have magnitudes of 1000psi. Determine the shear stress in the glue. Fixed End P 2 2 max = 1000psi 20 4 CROSS SECTION 4000lb 4000lb 50 psi 1 of 21

2. (40 points). The steel I-beam is considered to have failed if either: a. The normal bending stress exceeds 30 ksi, or b. The shear stress exceeds 15 ksi Problem: Determine the maximum uniform load w that may be applied without failure occurring. Given: The beam spans 50 inches over pin and roller supports. The cross-section is composed of 1 x 10 flanges and a ½ x 18 web, as shown. w =? 1 x 10 Flange ½ x 18 Web 50 inches 1 x 10 Flange 2 of 21

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1. (50 points) A box beam is fabricated from two plywood webs that are secured to the solid lumber boards at its top and bottom flanges. The beam supports a concentrated load of P=5000 lbs at the center of a 16-foot span. 3/8 diameter bolts connect the plywood webs and the solid lumber flanges at a spacing of 12 inches along the beam. Supports A and C are considered as a pin and roller. Determine: The maximum shear stress in the plywood webs. The average shear stress in the bolts. 12 8 ft 8 ft 4 of 21

1. (5 points). For which location would the shear forces on the nails be greatest (circle the correct answer)? Given: The left fixed support for the beam is denoted (1) and the right free end is denoted as (2). The nails on the top of the beam are denoted B and the nails on the bottom of the beam are denoted A. a. (1)A b. (1)B c. (2)A d. (2)B e. (1)A and (1)B (they are the same) w f. (2)A and (2)B (they are the same) (1) (2) 5 of 21

2. (45 points). Draw the stresses acting on element A shown, labeling their magnitudes and directions. Do not draw any other orientation (this is NOT a Mohr s Circle Problem): Given: The horizontal force of 5000 lbs is applied to the top of the cantilever beam at a distance that is 5 from the centerline of the beam, as shown. The beam has a 10 x10 cross-section 5000 lbs 5 2 A 3 70 30 10 x10 Cross Section 6 of 21

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1. (35 points) The timber beam is to be notched at its ends as shown. If it is to support the loading shown, determine the smallest depth d of the beam at the notch if the allowable shear stress is allow=450psi. The beam has a width of 8 inches. d 8 of 21

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4 (25 points) An 18-inch-long segment of a beam is shown. It is known to have a negative bending moment of 42 kip-in at point A and a negative bending moment of 36 kip-in at point B. Determine the resultant forces on each end of board number (1), then determine the shear stress that is in the glue that joins board (1) to board (3). (3) 10 of 21

5 (3 points) TRUE or FALSE. For the previous problem, the resultant normal force on board (1) is equal to the resultant normal force on board (2), at point B. 6 (3 points) TRUE or FALSE. For Problem 4, the resultant normal force on board (3) is zero at point B. 11 of 21

1. (10 points). Determine the shear stress between the top flange and the web of the I-beam shown. The beam is supported by a pin at A and a roller at B. It is subjected to 10 kip-in end-moments, as shown. There are no other applied loads. M = 10 kip-in M = 10 kip-in 4 x1 Flange A 100 B 4 x1 Flange Your job: find the shear stress here. 6 x1 Web Side View Cross-Section View 12 of 21

1. (35 points) For cross-section B-B, determine the maximum shear stress in the beam due to the applied loading. Given: Cantilever box beam with 10 x10 outside dimensions, 8 x8 inside dimensions. B w = 2 kip/ft 1 foot B 8 feet Cross-Section at B 10 x10 outside dimensions 8 x8 inside dimensions 13 of 21

2. (30 points) Beam ABCD is subjected to an unknown distributed load, as shown. The span is unknown. The distance between B and C is 10 inches. From strain gages that have been placed on the extreme top fiber, the strains at B and C are B = -1000 and C = -800. The beam is constructed of 4 x1 top and bottom flanges and 6 x1 web, all made of steel (E=30000 ksi) Determine: the average shear that is just below the top flange of the beam, between B and C. Loading is unknown A B C D Distance Unknown 10 Distance Unknown 4 x1 Flange 6 x1 Web Your job: find the shear stress here, between B and C 4 x1 Flange Cross-Section View 15 of 21

3000psi oil pressure behind the piston 3 diameter piston 2. (15 points). A rural water supply system consists of a water tank that is up on a hill, supplying water to a community in the valley. If the water level is at an elevation that is 100-ft above the community it supplies, determine the minimum wall thickness of the 4 diameter supply pipe needed so that the hoop stresses do not exceed 15 ksi. Given: a cubic foot of water weighs 62.4 lbs. Water Level 100-ft Water Tank 4 diameter water supply pipe 1. (5 points) A hydraulic jack is shown below, consisting of a 3 diameter piston that is inside a hollow cylinder. If the piston has 3000 psi oil pressure behind it, determine the maximum force P that this jack is capable of lifting. 3 diameter piston 17 of 21

2. (15 points). A rural water supply system consists of a water tank that is up on a hill, supplying water to a community in the valley. If the water level is at an elevation that is 100-ft above the community it supplies, determine the minimum wall thickness of the 4 diameter supply pipe needed so that the hoop stresses do not exceed 15 ksi. Given: a cubic foot of water weighs 62.4 lbs. 1. (40 points) Determine the maximum uniformly distributed load w (units: kips/inch) that may be applied to the beam without failing the glue that holds blocks (1) to block (2). Given: Blocks (1) are glued to Block (2). = 5.063 in (measured from the bottom), I=61.27 in 4 Blocks (1) are 1 x2, Block (2) is 6 x1, Block (3) is 6 x1 Max. allowable shear stress in glue = 1 ksi w =? (1) (2) (1) (3) 100 inches SIDE VIEW CROSS SECTION 18 of 21

2. (5 points). For the beam below, label the exact location at which the shear stress is maximum and briefly explain how you know this is the max point. w = 1 kip/ft 10 feet Cross-Section 19 of 21

5. (30 points) Determine the maximum shear stress that occurs in a weld. Given: Box beam with 12 x12 outside dimensions, and 10 x10 inside dimensions. The box beam is made by welding 4 plates together, at the locations shown. w = 1 kip/ft Welds 10 feet Cross-Section 12 x12 outside dimensions 10 x10 inside dimensions 1 wall thickness 20 of 21

(100 points) Determine the maximum uniformly-distributed load w (lbs/inch) that the T-beam can safely sustain, considering a) The normal stresses from bending, b) The shear stresses from bending, and c) The capacity of the fasteners that hold it together. The T-beam shown is made from two 3 x 10 wooden boards. The boards are fastened with lag screws that are spaced 3 apart. The allowable stresses and forces are as follows: Maximum allowable normal stress in the wood: allow = 1200 psi Maximum allowable shear stress in the wood: allow = 200 psi Maximum allowable (shearing) force in a lag screw: 1800 lbs. w (lbs/inch) 100 inches Cross-Section (2) 3 x 10 boards Held together with lag screws that are 3 apart 21 of 21