Question $1$: $($use SD procedures for all parts of this question$)$

A$.$ Find the nominal moment capacity of the beam section based on positive bending.

Assume that the area of reinforcing which is provided at the bottom of the section

is $2-$ #$5$ bars.

B$.$ Draw the stress$-$strain diagram for this cross$-$section $($corresponding to the basic

assumptions associated with the SD approach$),$ and label$/$identify the following:

a$.$ Tension & Compression force resultants:

b$.$ Max stresses and strains in the masonry and the rebar:

c$.$ Location of the neutral axis and the depth of the compression stress block.

C$.$ Find as for A$)$ above, but for negative bending moments, and assuming that the area

of reinforcing which is provided at the top of the section is $1-$ #$6$ bar.

D$.$ Do as for $B)$ above, but with the parameters associated with $C).$

E$.$ What is the maximum $($factored$)$ shear force which can be carried by the beam

cross$-$section, assuming that the masonry takes $100\%$ of the shear force?

F$.$ For the same beam section shown above, find the area of reinforcing which is

required at the bottom of the beam if a factored $($positive$)$ moment of $75ft.-$kips

is applied to the beam?

a$.$ Check min and max values for the area of steel which is provided via your

answer.

b$.$ For the area of steel which you have selected, what $\%$ of the balanced

reinforcing steel ratio is utilized via your design?

c$.$ Draw the stress$-$strain diagram for the design which you have selected, as

per the instructions in B$)$ above.