Question

1. For the cross section and loading shown below. [50 points] 10" fc-5500 psi 60,000 psi Concrete unit weight 150 pcf 18.5, P,-15 kips w 1,500 lb/ft 32" 25" 37 (12) #8 15" a. Calculate the gross moment of inertia, Ig, and the location of the centroid, ybar (from the bottom) Neglect the steel when calculating Ig. [10 points] b. What is the cracking moment, Mcr? [5 points] c. Calculate the cracked transformed moment of inertia, Icr. [10 points] d. What is the maximum service load moment, Ma, due to the applied loads above? [5 points] e. What is the effective moment of inertia, I.? [5 points] f. What is the instantaneous mid-span deflection for this beam due to dead and live load? [5 points] g. What is the additional long-term (over 5 years) mid-span deflection due to creep and shrinkage of the concrete? [5 points] h. According to ACI Ch. 24, are the deflections permissible if the member is supporting or attached to nonstructural elements not likely to be damaged by large deflections? [5 points]

Answer 1

gross Moment of Inertia cracking moment cracked transformed moment of inertia maximum service load moment
2s уг-글 ~ 3.sin 2 Mome rt 12 3 12 ha cing moment, Mcn Mer.fr-,- ss є 2 981 83.3 ab-in 二2.7 26.

5 S o r2 moment ahm depth lefoj, J. 3 2 〈 d)

e a Deod lo ad dus to e weight f t Ma