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# ch5-6 - SECTION 5.12 Beams with Axial Loads 363 Problem...

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Problem 5.12-10 A flying buttress transmits a load P 5 25 kN, acting at an angle of 60° to the horizontal, to the top of a vertical buttress AB (see figure). The vertical buttress has height h 5 5.0 m and rectangular cross section of thickness t 5 1.5 m and width b 5 1.0 m (perpendicular to the plane of the figure). The stone used in the construction weighs g 5 26 kN/m 3 . What is the required weight W of the pedestal and statue above the vertical buttress (that is, above section A ) to avoid any tensile stresses in the vertical buttress? Solution 5.12-10 Flying buttress SECTION 5.12 Beams with Axial Loads 363 60 ° P A A B B W h h t 2 Flying buttress t t F REE - BODY DIAGRAM OF VERTICAL BUTTRESS P 5 25 kN h 5 5.0 m t 5 1.5 m b 5 width of buttress perpendicular to the figure b 5 1.0 m g 5 26 kN/m 3 W B 5 weight of vertical buttress 5 bth g 5 195 kN C ROSS SECTION A 5 bt 5 (1.0 m)(1.5 m) 5 1.5 m 2 A T THE BASE N 5 W 1 W B 1 P sin 60º 5 W 1 195 kN 1 (25 kN) sin 60º 5 W 1 216.651 kN M 5 ( P cos 60º) h 5 (25 kN)(cos 60º)(5.0 m) 5 62.5 kN ? m T ENSILE STRESS ( EQUAL TO ZERO ) or 2 W 2 216.651 kN 1 250 kN 5 0 W 5 33.3 kN 52 W 1 216.651 kN 1.5 m 2 1 62.5 kN ? m 0.375 m 3 5 0 s t N A 1 M S S 5 1 6 bt 2 5 1 6 (1.0 m)(1.5 m) 2 5 0.375 m 3 60 ° P W h W B t N V M Problem 5.12-11 A plain concrete wall (i.e., a wall with no steel reinforcement) rests on a secure foundation and serves as a small dam on a creek (see figure). The height of the wall is h 5 6.0 ft and the thickness of the wall is t 5 1.0 ft. (a) Determine the maximum tensile and compressive stresses s t and s c , respectively, at the base of the wall when the water level reaches the top ( d 5 h ). Assume plain concrete has weight density g c 5 145 lb/ft 3 . (b) Determine the maximum permissible depth d max of the water if there is to be no tension in the concrete. h d t

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Solution 5.12-11 Concrete wall 364 CHAPTER 5 Stresses in Beams h 5 height of wall t 5 thickness of wall b 5 width of wall (perpendicular to the figure) g c 5 weight density of concrete g w 5 weight density of water d 5 depth of water W 5 weight of wall W 5 bht g c F 5 resultant force for the water pressure M AXIMUM WATER PRESSURE 5 g w d A 5 bt S TRESSES AT THE BASE OF THE WALL ( d 5 DEPTH OF WATER ) Eq. (1) Eq. (2) s c 52 W A 2 M S h g c 2 d 3 g w t 2 s t W A 1 M S h g c 1 d 3 g w t 2 S 5 1 6 bt 2 M 5 F ¢ d 3 5 1 6 bd 3 g w F 5 1 2 ( d )( g w d b ) 5 1 2 bd 2 g w (a) S TRESSES AT THE BASE WHEN d 5 h h 5 6.0 ft 5 72 in. d 5 72 in. t 5 1.0 ft 5 12 in. Substitute numerical values into Eqs. (1) and (2): s t 6.042 psi 1 93.600 psi 5 87.6 psi s c 6.042 psi 2 93.600 psi 99.6 psi (b) M AXIMUM DEPTH FOR NO TENSION Set s t 5 0 in Eq. (1): d max 5 28.9 in. d 3 5 (72 in.)(12 in.) 2 ¢ 145 62.4 5 24,092 in. 3 d 3 5 ht 2 ¢ g c g w 2 h g c 1 d 3 g w t 2 5 0 g w 5 62.4 lb / ft 3 5 62.4 1728 lb / in. 3 g c 5 145 lb / ft 3 5 145 1728 lb / in. 3 h d t M W F d/ 3 V
Eccentric Axial Loads Problem 5.12-12 A circular post and a rectangular post are each compressed by loads that produce a resultant force P acting at the edge of the cross section (see figure). The diameter of the circular post and the depth of the rectangular post are the same.

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ch5-6 - SECTION 5.12 Beams with Axial Loads 363 Problem...

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