Question $1($CLO$3)$

you have been tasked with fabricating several different reinforced concrete

beams. The cross$-$section design for the shear$-$deficient beam is presented in Figure $1$ below.

Assume fy for the stirrups and longitudinal reinforcing bars is $400$MPa.

Figure $1.$ CIVL$3230$ lab shear$-$deficient beam cross$-$section design $($Question $1)$

a$)$ Compute the shear resistance, $V_r,$ for the section within the shear span $($i$.$e$.,$ distance

between the support and first loading point$).$ Consider for both concrete compressive

strengths of $25$MPa and $40$MPa $($i$.$e$.,$ two separate calculations for each beam type$).$ Use

the shear provisions of CSA A$23\mathrm{.}3-19$ Cl$.11\mathrm{.}3$ which assumes material resistance factors for

concrete and reinforcing steel of ${}_c=0\mathrm{.}65$ and ${}_s=0\mathrm{.}85.$

b$)$ To predict the actual shear capacity of the beam $($i$.$e$.,$ when they are tested in flexure in the

lab$),$ you will need to compute the nominal shear resistance, $V_n$ where it is assumed that ${}_c$

$=1\mathrm{.}00$ and ${}_s=1\mathrm{.}00.$ Therefore, repeat your calculations in part a$)$ by computing $V_n$ for $25$

MPa and $40$MPa.