DesignExample4

DesignExample4 - 1.054/1.541 Mechanics and Design of...

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1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk 1 / 7 1.054/1.541 Mechanics and Design of Concrete Structures (3-0-9) Design Example Shear and Torsion Objective : To examine the adequacy of given cross section based on shear and torsion capacities. Problem : At a section of a beam, the internal forces are V u = 45 kips, M u = 300 kips-ft, and T u = 120 kips-ft. The material strengths are f’ c = 4 ksi and f y = 60 ksi. Assume that the distance from beam faces to the center of stirrups is 2 in and d is 21 in. a a Massachusetts Institute of Technology Figure 1 . Plan view of overpass 24 ‘’ 16 ‘’ T u M u V u Figure 2 . Cross section a-a
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1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk Design Example – Shear and Torsion Task : Answer or accomplish the following questions and tasks based on given assumption. Will this given cross section (16 in wide and 24 in deep) be adequate for shear and torsion requirements? If not, what width is required? Assume that the depth is to be held at 24 in. Select the required torsion, shear, and bending reinforcement for the minimum required width (to nearest inch). Summarize reinforcement on a sketch of the cross section. [Design Procedures] 1. Check maximum torsion capacity (ACI) For the given section: Section/(Equation) () 2 2 16 24 6144 xy == in 3 2 16 21 0.05469 6144 w T bd C = in -1 '2 3 22 0.8 0.8 4000 6144 318.88 10 0.4 45 0.4 1 1 0.05469 120 12 c c u Tu fx y T V CT = × ⎛⎞ + + ⎜⎟ ×× ⎝⎠ × lbs-in Since max 4 s c TT = 11.6.1 & () ( ) ( ) max 44 . 2 5 uc s c c c T T T T φφ ⇒= + = + = 0.85 ( for torsion) 11.6.2.2 φ = 3 max 1355 10 u T × lbs-in However, lbs-in 3
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DesignExample4 - 1.054/1.541 Mechanics and Design of...

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