Question $2(10$ Marks$)$

A typical cross$-$section of a reinforced concrete beam is shown in the figure below. Consider an

effective depth of $330mm.$ the concrete and steel materials properties are given below.

A$)$ Calculate the factored moment resistance for the beam section.

B$)$ If the contractor has accidently misplaced the reinforcing by $30mm,$ so that the effective

depth is reduced to $300mm,$ find the factored moment resistance for the beam section

considering the new reinforcement layout.

C$)$ If the actual $28-$ day concrete strength for the beam designed in part $($A$)$ is only $27$MPa.

Find the factored moment resistance for the beam section.

D$)$ Due to construction$-$related problems, the effective depth has been reduced to $300mm($as

in part $($B$))$ and the $28-$day concrete strength has reached only $27$MPa $($as in part $($C$)).$

find the corresponding moment resistance for the beam section.

E$)$ What conclusions can you draw from part $($A$)$ to $($D$)$ with regard to the effects of

construction errors on reinforcing bar placement and concrete strength respectively?

F$)$ Once you learned about the above construction errors, you reviewed the design

calculations and realized that there is a certain reserve in moment resistance of the beam

section. Which of the construction errors discussed in part $($B$)$ to $($D$)$ can be tolerated

when

$1-$ A $5\%$ reduction in the moment resistance value is acceptable.

$2-$ A $10\%$ reduction in the moment resistance value is acceptable.

G$)$ In spite of the specified tolerance, errors in the placement of reinforcement on the order

of $+-10\%$ are common in Canada, how would you attempt to compensate for these

construction errors in the design of reinforced concrete beams and slabs?

Given:

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

$f_y=400$MPa

${}_c=0\mathrm{.}65$

${}_s=0\mathrm{.}85$