$3\mathrm{.}6.$ A typical cross$-$section of a properly reinforced con$-$

crete beam is shown in the figure below. The material

properties are summarized below. Use an effective

depth of $650$ mm $.$

a$)$ Determine the factored moment resistance for

the following cases:

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

ii$)f_c^{\text{'}}=25$MPa

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

iv$)f_c^{\text{'}}=35$MPa

b$)$ Comment on the variation in concrete strength

on the moment resistance of the beam.

Given:

$f_y=400$MPa

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

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

$E_s=200000$MPa