Question $1[20$ points$]$

$($a$)$ List two limit states of strength and two limit states of serviceability in steel structures. $[2]$

$($b$)$ According to IS $800-2007,$ what are the partial safety factors for limit states of yielding $({}_{m0})$ and fracture $({}_{ml})?$ Why is one greater than the other? $[2]$

$($c$)$ Draw the possible plastic mechanisms for the uniformly loaded $2$ span continuous beam shown below. $[2]$

$($d$)$ According to IS $800-2007,$ the flexural strength $M_{dv}$ of a member subjected to high shear force is given by the following formula. What is $M_d$ and $M_{fd}?$ Justify the reasoning for the limit $1\mathrm{.}2\frac{Z_{fy}}{{}_{m0}}[2+2]$

$M_{dv}=M_d-(M_d-M_{td})1\mathrm{.}2Z_e\frac{f_v}{{}_{m0}}$ where $=(2\frac{V}{V_d}-1{)}^2$

$($e$)$ Explain the meaning of plastic, compact and semi$-$compact steel sections using plots only $[2]$

$($f$)$ Draw the moment$-$shear interaction diagram for compact or plastic sections $($fully restrained$).$ Which IS $800-2007$ provision regarding beam design results from this interaction diagram? $[2]$

$($g$)$ Draw a hot rolled I section and shade the shear area on it$.$ Plot the variation of shear stress with depth for the I section $[2]$

$($h$)$ According to IS $800-2007$ block shear strength is given by the following formulae. What is the source of the $0\mathrm{.}9$ and $\frac{1}{\sqrt[\phantom{2}]{3}}$ factors in these formulae? What are the two limit states signified in each formula? $[2+2]$

$T_{ob}=[A_{vg}\frac{f_y}{\sqrt[\phantom{2}]{3}{}_{m0}}+0\mathrm{.}9A_{tn}\frac{f_u}{{}_{m1}}]$

or

$T_{db}=(0\mathrm{.}9A_{vn}\frac{f_u}{\sqrt[\phantom{2}]{3}{}_{ml}}+A_{tg}\frac{f_y}{{}_{m0}})$

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