$2\mathrm{.}14$ Circle the correct statement$($s$)$ from the following:

a$)$ "Under$-$reinforced" beam condition results in a ductile failure mode.

b$)$ "Over$-$reinforced" concrete beam is acceptable because it is stronger than it needs to be and it is conservative.

c$)$ The failure mode of "under$-$reinforced" concrete beam is associated with brittle fracture.

d$)$ "Over$-$reinforced" beam corresponds to a condition where the beam maximum bending strength is controlled by

concrete cracking rather than steel yielding.

e$)$ The ACl code provisions include a maximum limit on the amount of beam reinforcing steel to ensure that an

"under$-$reinforced" condition exists.

$2\mathrm{.}15$ Compare the following three roof structures. All three have the same span length and the same total roof load.

Calculate the maximum bending moment at the main $($bottom$)$ beam. The beam has a rectangular cross$-$section

measuring $8-$inch wide by $12-$inch deep. Determine the maximum bending stress for all three cases for this beam.

Calculate the Section Modulus of the beam, S:

Calculate the maximum bend stress for

Uniformly distributed

Case $1$: Simple supported beam with uniformly distributed load