Question points$]$

The built$-$up beam shown in Figure $2$ is subjected to uniformly distributed load $w=10k\frac{N}{m}$ and has span length $l=10$ m$.$ Assume E$350$ steel and weld ultimate strength as $400$MPa

$($i$)$ If the web thickness is $6mm,$ what is the largest web depth allowed for design without stiffeners? The relevant condition in IS $800$ is where $=\sqrt[\phantom{2}]{\frac{250}{f_y}}[1]$

$($ii$)$ If the web thickness is $6mm,$ what is the largest web depth allowed so that buckling will not occur? The relevant condition in IS $800$ is $\frac{d}{t_w}<mn>6</mn><mn>7</mn><mi></mi><mi>[</mi><mn>1</mn><mi>]</mi>$

$($iii$)$ For the given loads and span, design a suitable flange width, flange thickness and overall beam depth. Total depth should not exceed $3000mm[3]$

$($iv$)$ For the given loads and span, design a suitable web depth and web thickness based on the chosen overall depth $1$

$($v$)$ For the given loads, design a shop fillet welded connection between flange and web. Assume partial safety factor ${}_{mm}=1\mathrm{.}25($shop welds$),$ design stress $f_{wd}=\frac{f_{wn}}{{}_{mw}},$ where $f_{wn}=\frac{f_{11}}{\sqrt[\phantom{2}]{3}},$ and $f_1$ is the smaller of ultimate stress of weld or parent metal $[3]$

$($vi$)$ Summarize the final cross section design for the given loads $[1]$

$($a$)$ Fixed$-$fixed beam for Question $2$ and Question $4.$iv

$($b$)$ Moment diagram,

$M_l=w\frac{l^2}{24},$

$M_{\text{m}\text{a}\text{x}}=w\frac{l^2}{12}$

$($c$)$ Shear force diagram, $V=w\frac{l}{2}$

$($d$)$ Beam built$-$up section

Figure $2$ : Built$-$up beam details for Question $2$ and $4.$iv