Determine the largest distributed dead load $w$ that can be supported by a fixed$-$fixed beam shown in Figure $1,$ assuming section size as $($a$)$ ISLB $450$ and $($b$)$ ISHB $250,$ steel grade as E$350,$ and span $l=10m$

Assumptions $/$ Hints:

$(1)$ Plastic mechanism may not be used. However, a single section may be allowed to reach plastic capacity $($if permitted by code$)$

$(2)$ Assume continuous lateral bracing

$(3)$ For serviceability, check whether the maximum service deflection is within Span$/360.$ Peak deflection of a fixed$-$fixed beam of span $l$ with distributed load $w$ is $w\frac{l^4}{384EI},$ where the symbols have their usual meaning

$(4)$ Ignore self$-$weight of the beam

$(5)$ Cross section properties are given in Question $2$

$($a$)$ Fixed$-$fixed beam for Question $3$ and

$($b$)$ Moment diagram,

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

Question $4$

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

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

Figure $1$ : Fixed$-$fixed beam, moment diagram and shear force diagram