Question

Question 16 A6 ft long A36 steel W12x14 carries a uniform load as shown. Assume all stresses remain linear elastic. 2 kip/ft A B C 3 ft 3 ft The deflection at A is most nearly.... 0.014 in 0.032 in 0.189 in 1.193 in

Answer 1

Given that w = 2 kil/ft MBT akip-ft mm A C Ronzo 3 ft *ال 비 Roy 2.6 kip from the eauilibrium Conditions Efno RB x=0 Efyzo RBy = (2) (3) RBY = 6 kip EMB=0 MB (2) (3) (rs) MB za kip-ft .btw C&A 2) Now Consider a section x-X at a distana ag from B. M = 9 kip-ft W = 2kiplet G c Mr M = (6) (nro) + nanog (2)(x-3)² - - (2) Cr-o)? Roy = 6 kip K - 962-0) from the defection eavation 2 2 به EI day +КС dra

=) (EJ) ( ) --2 G1-0) 26-3) 2 6(2-0). dne + -QCn-o)' =) EI dý da? (+3)² +66-0)- G-od 2 a (a-ojo = ) EI dy doc du jo (4-3) 3+ (2-3) 34 6(4-0)2 4-0)} +0,960) EI (Y) = (21-334 + 3 (on-0)3 (n-olu & Cia 12 3 Boundary Condition ③ -9 (0-0) 2 +C2 at no an dy =0 - Gi=0 for a singularity function -ah, 9 Boundary Condition 2 & G-a)n neza o nea at n=0 ; yzo (2=0. (EI) (y) = (x-3) 4 + Gn-o) 3 (no) 12 _962-0² 12 2 foor A36 Skeel a young's modolog E = 29000 ksi for a beam's ols W 12x4. -) area moment of inertia of the cross-section

about the Centroidal anis is. مرے ہل 88.6 iny X-X -> (63)(y) 61-3) " (x-2)} _ (x-o)" + a On-o)? 12 12 2 at na 6ft = 72 in » deflection at A is 2 (29x166) (88.6) (y) (6-3) 4 (6)} 64 12 () C6 12 (29x106)(88.6) Cy) = -47.25 -47.25m lbf, fk3 x 103 = -47.25 X103 Ibf-in3 -) YA = 0.077 in -0.0319 at x = 3ft 3 de fieofion af ' is, (29x106) (88.6) (y) = for(3) 3 - 34 **** ]mce Jr x 103 x 1²23 -9 (3) Yos-00136 in