05-01ChapGere.0018 - 302 A-PDF Stresses in Beams (Basic...

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Problem 5.5-22 A cantilever beam AB with a rectangular cross section has a longitudinal hole drilled throughout its length (see figure). The beam supports a load P 5 600 N. The cross section is 25 mm wide and 50 mm high, and the hole has a diameter of 10 mm. Find the bending stresses at the top of the beam, at the top of the hole, and at the bottom of the beam. Solution 5.5-22 Rectangular beam with a hole 302 CHAPTER 5 Stresses in Beams (Basic Topics) 50 mm 12.5 mm 25 mm 10 mm AB P = 600 N L = 0.4 m 37.5 mm M AXIMUM BENDING MOMENT M 5 PL 5 (600 N)(0.4 m) 5 240 N ? m P ROPERTIES OF THE CROSS SECTION A 1 5 area of rectangle 5 (25 mm)(50 mm) 5 1250 mm 2 A 2 5 area of hole A 5 area of cross section 5 A 1 2 A 2 5 1171.5 mm 2 Using line B-B as reference axis: A i y i 5 A 1 (25 mm) 2 A 2 (37.5 mm) 5 28,305 mm 3 Distances to the centroid C : c 1 5 50 mm 2 c 2 5 25.838 mm c 2 5 y 5 24.162 mm y 5 a A i y i A 5 28,305 mm 3 1171.5 mm 2 5 24.162 mm 5 p 4 (10 mm) 2 5 78.54 mm 2 M OMENT OF INERTIA ABOUT THE NEUTRAL AXIS
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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