Problem $1.$

A heavy$-$duty plant has a roof truss with span of $80$ meter, the column spacing is $12m.$ given the characteristic value of live load is $q_k=0\mathrm{.}5k\frac{N}{m^2}.$ You asked to

$(1)$ estimate the characteristic value of self$-$weight load $g_k$ of frame truss $($area load, unit: $($:$k\frac{N}{m^2}\}$

$(2)$ estimate the design value of area load q of roof $($area load, unit: $k\frac{N}{m^2})($hint: consider permanent load and live load in load combination$)$;

$(3)$ estimate the design value of line load $q_L$ on frame truss $($line load, unit: $k\frac{N}{m})$

$(4)$ estimate the equivalent concentrated point load $Q_A$ and $Q_B,($due to $q_L)$ on frame truss node A and $B.$

$q_k$

$g$