02-01ChapGere.0016

# 02-01ChapGere.0016 - d AC is not to exceed 4.0 mm P 1 = 400...

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78 CHAPTER 2 Axially Loaded Members b 4 b P P L 2 L 4 L 4 t 5 thickness L 5 length of bar (a) E LONGATION OF BAR 5 PL Ebt ¢ 1 4 1 4 6 1 1 4 5 7 PL 6 Ebt d 5 a N i L i EA i 5 P ( L / 4) E ( bt ) 1 P ( L / 2) E ( 3 4 bt ) 1 P ( L / 4) E ( bt ) S TRESS IN MIDDLE REGION S UBSTITUTE INTO THE EQUATION FOR d : (b) S UBSTITUTE NUMERICAL VALUES : d 5 7(24,000 psi)(30 in.) 8(30 3 10 6 psi) 5 0.0210 in. E 5 30 3 10 6 psi s 5 24,000 psi Ê L 5 30 in. 5 7 s L 8 E d 5 7 PL 6 Ebt 5 7 L 6 E ¢ P bt 5 7 L 6 E ¢ 3 s 4 s 5 P A 5 P ( 3 4 bt ) 5 4 P 3 bt Ê or Ê P bt 5 3 s 4 Problem 2.3-6 A two-story building has steel columns AB in the first floor and BC in the second floor, as shown in the figure. The roof load P 1 equals 400 kN and the second-floor load P 2 equals 720 kN. Each column has length L 5 3.75 m. The cross-sectional areas of the first- and second- floor columns are 11,000 mm 2 and 3,900 mm 2 , respectively. (a) Assuming that E 5 206 GPa, determine the total shortening d AC of the two columns due to the combined action of the loads P 1 and P 2 . (b) How much additional load P 0 can be placed at the top of the column (point C ) if the total shortening
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Unformatted text preview: d AC is not to exceed 4.0 mm? P 1 = 400 kN P 2 = 720 kN B A C L = 3.75 m L = 3.75 m Solution 2.3-6 Steel columns in a building P 1 = 400 kN P 2 = 720 kN B A C L L L 5 length of each column 5 3.75 m E 5 206 GPa A AB 5 11,000 mm 2 A BC 5 3,900 mm 2 (a) S HORTENING d AC OF THE TWO COLUMNS d AC 5 3.72 mm 5 1.8535 mm 1 1.8671 mm 5 3.7206 mm 1 (400 kN)(3.75 m) (206 GPa)(3,900 mm 2 ) 5 (1120 kN)(3.75 m) (206 GPa)(11,000 mm 2 ) Ê d AC 5 a N i L i E i A i 5 N AB L EA AB 1 N BC L EA BC Problem 2.3-5 Solve the preceding problem if the axial stress in the middle region is 24,000 psi, the length is 30 in., and the modulus of elasticity is 30 3 10 6 psi. Solution 2.3-5 Bar with a slot A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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