For all questions in this problem set:

Maximum aggregate size $=20mm$

$f_y=400$MPa

interior exposure

shear steel in all cases $=$#$10$ bar

You should check bar spacing details but ignore crack control

Note in my solutions I used the bar # as the bar diameter. Using the true bar diameters will change the answers slightly. Either way, I count it as the right answer.

Note that $f^{\text{'}}$ c varies form question to question.

QUES:

Design the singly reinforced rectangular concrete beam for bending moment reinforcement only. Design the beam for approximately $50\%$ of balanced steel.

ANSWERS:

Final beam: $h=800mm.,b=630mm.,d=737\mathrm{.}5mm,$ shear steel $=$ # $10$ bars, moment rebar $=7$ @ $35M$ bars $M_r=1542KN-m>M_F=1519KN-m$ therefore ok$,$ actual bar spacing $=49mm,$ required bar spacing $=49mm$ therefore ok: actual reinforcement ratio of balanced $+1\mathrm{.}5\%$ of targ et therefore ok

QUESTION #$3$ Given $f_c^{\text{'}}=35$MPa

Find the value of $Mr$ for the singly reinforced rectangular concrete beams for each case:

a$)300500$ cross section $(bh)$ with $4-$#$20$ bars moment reinforcement. Shear steel $=$#$10$

b$)400700$ cross section $(bh)$ with $5-$ #$25$ bars moment reinforcement. Shear steel $=$#$10.$

ANSWERS:

$M_r=503KN-m,$

bar spacing $=49mm>35mm$ required therefore $OK$