Problem $1$: Table $2\mathrm{.}1$ Reinforcement ratio $(Y)$ for rectangular sections

with tension reinforcement $f_y=400$MPa

$M=K_{c}b{d}^0{10}^{-6}kN-m_{\text{;}},K_r=[1-\frac{{}_d{f}_r}{2a_1{}_c{f}_i}]{}_1{f}_y,=\frac{A_1}{bd}$ Table $2\mathrm{.}1($Cont$\text{'}$d$)$ Table $2\mathrm{.}1($Cont$\text{'}$d$)2-24$ Table $2\mathrm{.}1($Cont$\text{'}$d$)$

A typical cross section of a properly$-$designed reinforced concrete beam is shown below. Using

the basic principles, the following is required:

a$)$ Determine the factored moment resistance for the following cases:

i$.f_c^{\text{'}}=20$MPa

ii$.f_c^{\text{'}}=30$MPa

iii. $f_c^{\text{'}}=40$MPa

iv$.f_c^{\text{'}}=50$MPa

b$)$ If$,$ due to a construction error, the steel reinforcement was misplaced such that the

effective depth of the beam is reduced to $585$ mm $.$ What is the factored moment

resistance considering the new reinforcement layout? Comment on the effect of changing

the effective depth on the moment resistance of the beam. $($Consider $f_c^{\text{'}}=35$MPa $)$

c$)$ If the beam is simply supported over a span of $6\mathrm{.}0$ m $,$ determine the safe uniformly

distributed live load and superimposed dead load that the beam can carry. The

superimposed dead load to live load ratio is $0\mathrm{.}8.($Consider $f_c^{\text{'}}=35$MPa and ${}_c=24\mathrm{.}0$

$k\frac{N}{m^3})$

Material Properties:

$f_y=400$MPa

$E_s=200,000$MPa

Problem $2$:

For the cross section shown in problem $1,$ determine the moment resistance when $f_c^{\text{'}}=40$MPa

using the CDH method. Compare the result with that from problem $1.$