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 = 5 ft. LBC = 2 ft, LCD= 3 ft, LDE = 4 ft, Pc = 2060 lb, Pe= 1990 lb, WAB = 750 lb/ft, b1 = 10 in., b2 = 2 in., b3 = 7 in., dų = 2 in., d2 = 8 in., d3= 2 in. Consider the entire 14-ft length of the beam and determine: (a) the maximum tension bending stress or at any location along the beam, and (b) the maximum compression bending stress oc at any location along the beam. Pc PE WAB x O D E B LBC LAB LCD LDE bi d d2 b2 dz b3

Answer 1

~ centroid location Solution in y-direction: Trin y 10 in 2 8 in 2 in 2 in K Fin shape Area (Ail yi 9: Ai (3) (from batom) (in Top flange 20 Il 220 Web 16 6 96 bottom flange 14 1 14 soin2 33 0 In Eyii 330 = 6.6 in (from bottom of so shape to centroid) - 5.4 in (trom top of shape to centroid) Moment of inertia about a anks :- d=yi- Ic. (iny 2A Ict d2A shape (inu) Top flange 6.6667 4.4 387. 2 393.8667 Web 85,3333 -0.6 5.76 91.033 bottom flange 4.6667 1-5.6 439.04 443.7067 Moment of inertia about the zoonis (in) = 928.66672 in

Draw shear farce & bending-moment diagrams- 750 lb/ft 2060eb 1990 lb KI B D € * 2634, Seb 356 S165.soft 2634.5 1990 lb (V) (16) @ X = 3.512737 -liis.5 - 3175,5 9627.058 (N ebote) 377.5 12566.5 - 7960 Morimum bending moments ! - posetive M = 4627,038 lbett Negative Me -760 lb.tt Bending stresses at mox positive moment - • Be (4627,058/b.ft) (siyon (12 in /h) 928.66673 in 4 x = 322.56 psi (c) (4627.058) (-666) (12) 928. 66673 x = 394.612 psi CT) - Bending stresses at negative moment :- ba man

Thank you.