Question

A flanged wooden shape is used to support the loads shown on the beam. The dimensions of the shape are shown in the second figure. Assume LAB = 7 ft, Lec = 4 ft, Lcd = 4 ft, LDE = 2 ft, Pc = 1730 lb, PE = 2320 lb, WAB = 710 lb/ft, b = 8 in., b2 = 2 in., b3 = 5 in., da = 2 in., d2 = 7 in., dz = 2 in. Consider the entire 17-ft length of the beam and determine: (a) the maximum tension bending stress of at any location along the beam, and (b) the maximum compression bending stress oc at any location along the beam. WAB B C D E LBC* - LCD LDE * 22 b2

Answer 1

1730 06 23901b 710 U/ht Em --- C D E t 746 4 4 4 2 ft * TM centroid location in Yo direction Shape Area (A) from bottom top flange 8x2, 16:2 web 7214 WWW 7+2+3) - 10m 2.1 5.5. Ž lim bottom flange Sp2 -10 2 A; - 40 in 2 EA4, = 247 mm EA;Y; 247_ - n 6.175 in ( from bottom) 40 EA i ; 4.825cm ( from top ) M.O. - shape Iabout z-axis: I I I d= 9; - ý dÅ I It da . a top flange 5.333 3.825 234.09 239.423 web 57. 1667 -0.675 6.3787 63.545 - 5.175 3.333 267.806 bottom flange 271. 139

i moment of inertia about Z-axis : 239.423 + 63.545 + 271.139 ) = 574.107 im4 710 Ulft 1730 lb 232016 A C 90 E 75 B to 4ft 4ft 24 3962-33 2320 Shear force diagram -1007.67 -2737.67 11056.4 10341.33 6310.67 Bending moment diagram -4640 maximum bending moments positive M = 11056.4 c6.ft negative M2 -4640 b.ft 3 Bending stress @ mar.positive moment - (1056.4 86.68) (-6.175 m) ( 12 in/50) = 1427. 049 574.107 in"

is maximum tension bending stress , 1427.049 pi (b) Bending stress @ mar. negative moment (-4640) - (- %) (12) 5740107 467.954 578/888 a max. compression bending stress : 467.954 psi 69%88% pusi UUUUUUUUUUUUUUUUU