Explanation Given information: The x ′ and y ′ axes are the principal centroidal axes of the cross section. Calculation: Refer to Figure P6.81 in the text book. I x ′ = 1.428 t a 3 I y ′ = 0.1557 t a 3 β = 15.8 ° Sketch the cross section of the angle section as shown in Figure 1. Refer to Figure 1. Area of the member A ( y ) = ( 2 a − y ) t . Centroid of the member. y ¯ = 1 2 ( 2 a + y ) x ¯ = 0 Calculate the shear along the centroidal axes as shown below. Along x ′ axis: V x ′ = P cos β Substitute 15.8 ° for β . V x ′ = P cos 15.8 ° = 0.9622 P Along y ′ axis: V y ′ = − P sin β Substitute 15.8 ° for β . V y ′ = − P sin 15.8 ° = − 0.2723 P Calculate the centroid along the centroidal axes as shown below. Along y ′ axis: y ′ ¯ = ( y ¯ − 2 3 a ) cos β − ( x ¯ − 1 6 a ) sin β Substitute 1 2 ( 2 a + y ) for y ¯ , 0 for x ¯ , and 15.8 ° for β . y ′ ¯ = ( 1 2 ( 2 a + y ) − 2 3 a ) cos 15.8 ° − ( 0 − 1 6 a ) sin 15.8 ° = 0.9622 ( a + y 2 − 2 3 a ) + 0.0454 a = 0.3207 a + 0.4811 y + 0.0454 a = 0.3661 a + 0.4811 y Along z ′ axis: x ¯ ′ = ( x ¯ − 1 6 a ) cos β + ( y ¯ − 2 3 a ) sin β Substitute 1 2 ( 2 a + y ) for y ¯ , 0 for x ¯ , and 15.8 ° for β . x ¯ ′ = ( 0 − 1 6 a ) cos 15.8 ° + ( 1 2 ( 2 a + y ) − 2 3 a ) sin 15

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Chapter 6.6, Problem 81P

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The distribution of the shearing stresses along line D′B′ in the horizontal leg of the angle shape.

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Chapter 6.6, Problem 80P

Chapter 6.6, Problem 82P

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Chapter 6 Solutions

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Ch. 6.2 - Three full-size 50 100-mm boards are nailed...Ch. 6.2 - For the built-up beam of Prob. 6.1, determine the...Ch. 6.2 - Three boards, each 2 in. thick, are nailed...Ch. 6.2 - A square box beam is made of two 20 80-mm planks...Ch. 6.2 - The American Standard rolled-steel beam shown has...Ch. 6.2 - The beam shown is fabricated by connecting two...Ch. 6.2 - A column is fabricated by connecting the...Ch. 6.2 - The composite beam shown is fabricated by...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...

Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.13 and 6.14 For a beam having the cross section...Ch. 6.2 - 6.13 and 6.14 For a beam having the cross section...Ch. 6.2 - For a timber beam having the cross section shown,...Ch. 6.2 - Two steel plates of 12 220-mm rectangular cross...Ch. 6.2 - Two W8 31 rolled sections may be welded at A and...Ch. 6.2 - For the beam and. loading shown, determine the...Ch. 6.2 - Fig. P6.19 6.19 A timber beam AB of length L and...Ch. 6.2 - A timber beam AB of Length L and rectangular cross...Ch. 6.2 - 6.21 and 6.22 For the beam and loading shown,...Ch. 6.2 - 6.21 and 6.22 For the beam and loading shown,...Ch. 6.2 - 6.23 and 6.24 For the beam and loading shown,...Ch. 6.2 - 6.23 and 6.24 For the beam and loading shown,...Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.2 - Prob. 27P Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.5 - The built-up timber beam shown is subjected to a...Ch. 6.5 - The built-up beam shown is made by gluing together...Ch. 6.5 - The built-up beam was made by gluing together...Ch. 6.5 - Several wooden planks are glued together to form...Ch. 6.5 - The built-up wooden beam shown is subjected to a...Ch. 6.5 - Knowing that a W360 122 rolled-steel beam is...Ch. 6.5 - 6.35 and 6.36 An extruded aluminum beam has the...Ch. 6.5 - 6.35 and 6.36 An extruded aluminum beam has the...Ch. 6.5 - Knowing that a given vertical shear V causes a...Ch. 6.5 - The vertical shear is 1200 lb in a beam having the...Ch. 6.5 - The vertical shear is 1200 lb in a beam having the...Ch. 6.5 - 6.40 and 6.47 The extruded aluminum beam has a...Ch. 6.5 - Prob. 41P Ch. 6.5 - Prob. 42P Ch. 6.5 - Three planks are connected as shown by bolts of...Ch. 6.5 - A beam consists of three planks connected as shown...Ch. 6.5 - A beam consists of five planks of 1.5 6-in. cross...Ch. 6.5 - Four L102 102 9.5 steel angle shapes and a 12 ...Ch. 6.5 - A plate of 14-in. thickness is corrugated as shown...Ch. 6.5 - Prob. 48P Ch. 6.5 - An extruded beam has the cross section shown and a...Ch. 6.5 - Prob. 50P Ch. 6.5 - The design of a beam calls for connecting two...Ch. 6.5 - The cross section of an extruded beam is a hollow...Ch. 6.5 - Prob. 53P Ch. 6.5 - Prob. 54P Ch. 6.5 - Prob. 55P Ch. 6.5 - 6.56 and 6.57 A composite beam is made by...Ch. 6.5 - 6.56 and 6.57 A composite beam is made by...Ch. 6.5 - Prob. 58P Ch. 6.5 - Prob. 59P Ch. 6.5 - Prob. 60P Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - Prob. 64P Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.69 through 6.74 Determine the location of the...Ch. 6.6 - Prob. 70P Ch. 6.6 - Prob. 71P Ch. 6.6 - Prob. 72P Ch. 6.6 - Prob. 73P Ch. 6.6 - Prob. 74P Ch. 6.6 - Prob. 75P Ch. 6.6 - 6.75 and 6.76 A thin-walled beam has the cross...Ch. 6.6 - 6.77 and 6.78 A thin-walled beam of uniform...Ch. 6.6 - Prob. 78P Ch. 6.6 - Prob. 79P Ch. 6.6 - Prob. 80P Ch. 6.6 - Prob. 81P Ch. 6.6 - Prob. 82P Ch. 6.6 - Prob. 83P Ch. 6.6 - Prob. 84P Ch. 6.6 - Prob. 85P Ch. 6.6 - Solve Prob. 6.85, assuming that the thickness of...Ch. 6.6 - Prob. 87P Ch. 6.6 - Prob. 88P Ch. 6 - Three boards are nailed together to form the beam...Ch. 6 - For the beam and loading shown, consider section...Ch. 6 - For the wide-flange beam with the loading shown,...Ch. 6 - For the beam and loading shown, consider section...Ch. 6 - The built-up timber beam is subjected to a 1500-lb...Ch. 6 - Knowing that a given vertical shear V causes a...Ch. 6 - Three planks are connected as shown by bolts of...Ch. 6 - Three 1 18-in. steel plates are bolted to four L6...Ch. 6 - The composite beam shown is made by welding C200 ...Ch. 6 - Prob. 98RP Ch. 6 - A thin-walled beam of uniform thickness has the...Ch. 6 - Determine the location of the shear center O of a...

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