$1.$ Design the singly reinforced beam below for the most efficient section $($Es$=0\mathrm{.}005)$ for the following loads: MD$=90$kNm and ML$=200$kNm$.$ The concrete strength is f$$c$=34\mathrm{.}5$MPa, the steel yield stress is fy$=400$MPa, and the steel modulus of elasticity is as usual, $200000$MPa. The clear cover from the bottom of the beam to the edge of the steel and from the side of beam to the edge of the steel must be at least $40$mm$,$ and not greater than $75$mm$.$ Clear distance between individual bars must be $25$mm or the bar diameter, whichever is larger. Present the result of your design in a sketch, showing the total required steel area, number and size of bars, depth to tension steel and total section height. Conduct a section analysis of your final design to confirm its capacity.

$2.$ Determine the required area of tension steel for the beam cross section shown below and the corresponding number, size, and location of bars. The loads are: MD$=160$kNm and ML$=410$kNm$.$ The concrete strength is f$$c$=41\mathrm{.}5$MPa, the steel yield stress is fy$=420$MPa, and the steel modulus of elasticity is as usual, $200000$MPa. The clear cover from the bottom of the beam to the edge of the steel and from the side of beam to the edge of the steel must be at least $40$mm$,$ and not greater than $75$mm$.$ Clear distance between individual bars must be $25$mm or the bar diameter, whichever is larger. Conduct a section analysis of your final design to confirm its capacity. Problem $1$: Design the singly reinforced beam below for the most efficient section $(s=0\mathrm{.}005)$

for the following loads: $MD=90kNm$ and $ML=200kNm.$ The concrete strength is $f^{\text{'}}c=34\mathrm{.}5$MPa, the

steel yield stress is $f_y=400$MPa, and the steel modulus of elasticity is as usual, $200000$ MPa $.$ The

clear cover from the bottom of the beam to the edge of the steel and from the side of beam to the

edge of the steel must be at least $40$ mm $,$ and not greater than $75$ mm $.$ Clear distance between

individual bars must be $25$ mm or the bar diameter, whichever is larger. Present the result of your

design in a sketch, showing the total required steel area, number and size of bars, depth to tension

steel and total section height. Conduct a section analysis of your final design to confirm its

capacity.

Problem $2$: Determine the required area of tension steel for the beam cross section shown

below and the corresponding number, size, and location of bars. The loads are: MD $=160kNm$

and $ML=410kNm.$ The concrete strength is $f_c^{\text{'}}=41\mathrm{.}5$MPa, the steel yield stress is $f_y=420$MPa,

and the steel modulus of elasticity is as usual, $200000$ MPa $.$ The clear cover from the bottom of

the beam to the edge of the steel and from the side of beam to the edge of the steel must be at

least $40$ mm $,$ and not greater than $75$ mm $.$ Clear distance between individual bars must be $25$ mm

or the bar diameter, whichever is larger. Conduct a section analysis of your final design to

confirm its capacity.