05-02ChapGere.0013

05-02ChapGere.0013 - 316 A-PDF Stresses in Beams (Basic...

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Problem 5.6-19 A steel plate (called a cover plate ) having cross- sectional dimensions 4.0 in. 3 0.5 in. is welded along the full length of the top flange of a W 12 3 35 wide-flange beam (see figure, which shows the beam cross section). What is the percent increase in section modulus (as compared to the wide-flange beam alone)? Solution 5.6-19 Beam with cover plate 316 CHAPTER 5 Stresses in Beams (Basic Topics) 4.0 3 0.5 in. cover plate W 12 3 35 All dimensions in inches. W IDE - FLANGE BEAM ALONE (A XIS 1-1 IS CENTROIDAL AXIS ) W 12 3 35 d 5 12.50 in. A 0 5 10.3 in. 2 I 0 5 2.85 in. 4 S 0 5 45.6 in. 3 B EAM WITH COVER PLATE ( z AXIS IS CENTROIDAL AXIS ) A 1 5 A 0 1 (4.0 in.)(0.5 in.) 5 12.3 in. 2 First moment with respect to axis 1-1 : 5 13.00 in. 3 c 2 5 6.25 1 y 5 7.307 in. c 1 5 6.25 1 0.5 2 y 5 5.693 in. y 5 Q 1 A 1 5 13.00 in. 3 12.3 in. 2 5 1.057 in. Q 1 5 a y i A i 5 (6.25 in. 1 0.25 in.)(4.0 in.)(0.5 in.) Moment of inertia about axis 1-1 : 5 369.5 in. 4 Moment of inertia about z axis: I z 5 369.5 in. 4 2 (12.3 in. 2 )(1.057 in.) 2 5 355.8 in. 4 S ECTION MODULUS (Use the smaller of the two section moduli) I NCREASE IN SECTION MODULUS Percent increase 5 6.8% S 1 S 0 5 48.69 45.6 5 1.068 S 1 5 I
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