Question

2.5" 2#7 fc= 4,000 psi fy= 60,000 psi n 8 5#11 3" 18" For service level moment M= 200 ft-k, use the procedures from Chapter 2 to find (20 pts) the following using linear-elastic analysis procedures and using transformed section a. properties: compressive stress in the concrete (fc) tension stress in the bottom steel (fs) compressive stress in the top steel (f's) What is the applicable moment of inertia of the concrete section if the (10 pts) service level moment is less than 65 ft-k using the procedures from Chapter 2. b. Using the proced u res from Chapter 5, analyze the given section to determine the C. (20 pts) reliable flexural design capacity (o Mn) (ultimate moment capacity). Verify any assumption. 18.5"

Answer 1

la) Lorating neutras asin 028 Mz200 ft-k 18* X + (24-1) 1-2 (2-2.5 ) = 8x7.8 x (21-X) 90 + 27:62-69 = 1310.4 - 62.42 (2n-1) 18 247(124) -Hissin 21-4 9x + 90x- 1379.4 = 0 OC - 8.35 in Moment of Inertian 1.1*1848.35"+ (24-1) 12 (8-35-2.5) +8x78x621-8-35 3466005 is 4 Bending stresses (7.80) SH 11 nas k 18 Transformed section to? fca My , 12x200 x 18x8.35 = 4300.38 pri ? 4660-05 12x200 410 4 (8.35-2.5 48205.49 pri In my 29 2x8 x 12 x 200 x003, re 4660-65 52119.61 psi dsa 8x12x200 x 18 x (21-8.35) cs-Scanned with CamScanner 4660-05

(C) Astumins fy = ty Asdy a 0.85 fb B, C + nády 27 (12 in ) 18:57 (7 ) r 78 x 60 = 0-85*4 x 18x085 C + 12x66 C = 7.61 is a = Bic: 0.88x7.61 = 6.47 in SH11 18.1) - e C-d' 0.003 - 7.61-25 X0:003 = 0.00 201 761 0.00 207 > Ene Sy 260.000 E 29,000,000 &' & dy as assumed As dy z o8ssa pieb + As (C-d! x0003] Es 0.00 3 x 29000 (c. 7.8x60 z 0.85X 4 X 0.85 x 18 c + 1.2 468 52 02 C + 104.40 - 261 468C: 52-02 C + 104-40 - 261 52.02ě - 363.6c-961=0 c= 7.64 in a=0.85 x 7.64 649 in Es: C-d'X0-0032 7.64 -2.5 10.003 = 0.00201 Lty 764 f2E ERZ0-00201 x 29000 = 58.53 km As 2 = Asts 1.20 x 58530 2 1.17 is ty 60 OCD Asi As-As 2 = 78 - 1.17 = 6.63 is d-CX0.003 764 Ez d-CX0:003 = 21-7-64 x0003 20.0052 20 00S id=0.9 Omn & (As, dy (d-a) + As ds (d-d')] -0.9( 663x60 x (91-6-49) + 12x 58-53 (21-25)] 2 7526-07 is_k : 627. 17 ft k Scanned with CamScanner