Question

ARC2580 STRUCTURES 1 HOMEWORK DUE 1-1-20 S. BRASGALLA, INSTRUCTOR NAME Problem 5. THIS IS A SOUTHERN PINE No. 2 WOOD BEAM, NOMINAL 4 X 12. THIS BEAM SPANS 16 FEET AND CARRIES A LOAD OF 300 LBS. PER FOOT ALONG ITS LENGTH. CALCULATE THE MAXIMUM BENDING STRESS AND THE MAXIMUM SHEAR STRESS GENERATED IN THIS BEAM. NEUTRAL AXIS

Answer 1

300 Lbs A 7 12" 8 2 B it 16 feet i 4800Lbs с RB 8 feet RAT 24oolba 5.F.D 1 BM.D 2400lb, Asszeobt 96c0 1152oolbs-in. - Cust og A & B i-e. RA E calculating recections at UDL to point load pt = 300x16 , = 4800lbs. Lic RA - 4800 t Ro=0 RA +R B = 4800 lbs. - - taking moment about point A EMA (4800)X(85 - RB X16 Ro= 4800 x 8 = 2.400 lb X 6

4800 > ven section. put in eg? RA + 2400 RA=24oolbs S. F. calculation sif.at A. RA 24oolbs s. E at B RB = -24.00 lbs So at a & 24 RA&-(300x 8) 2400-2400.20 Maximum S. f. is at reactions ie at RA & RB. = 2400 lbs for given C. V-2400 lbs Aittas *) Now marimum shear stress induced in beam is. vo T. where I b r = shear force 4 Q = static moment force b = width of boom I = moment of inertia 19 WKT, mar shear stress is incluced at neutral aris, si a Q = EAG =16* 4) x (3) il 3 72 in bh 12 D] H 4x122 12 576in b = 4

Tmax 2400 x 72 576x4 Tonca or.o.5) mpa. 75 lbstina * Now, marximum bending moment mazimun bending soment in given is at centre &. where shear force changes to i.e. shear force no beam its sire, sign. Bendi ing MB co M. at A & B. e B.M at a Max.B.M. Mc = 2400X8 - (300x 8) 4 Mc = 9600 lbs-foot 4" stress.oob maximum bend bending st ob= My X NA I from the a M B.M y = vertical distance away neutral axis I = Moment of inertia. ob 1200 = 9600X12 x 6 576 ob 1200 lbs/in² 07 8.2 Alpa stress in wooden beam is max. bending