$\backslash$table$[[$H$,$H$,$H$],[$H$,$H$,$H$],[$H$,,$H$],[$H$,$H$,$H$]]$

Fig. $3$ Fig. $4$Fig. $5$ shows construction

detalls of the retrofitting

Fig. $5$

DETAIL. AProblem $3$

Given an existing two$-$story steel structure with interior columns spaced as shown in Fig.

The columns are spaced at $18ft$ in the North$-$South direction and at $30ft$ in the East$-$

West direction. An interior lower$-$story column is to be removed by adding new steel

girder as shown in Fig. $4.$ The floor dead loads and the roof dead loads are $70psf$ and $18$

psf respectively. The floor live loads and the roof live loads are $50psf$ and $20psf$

respectively. All existing steel materials are ASTM A$36$ steel $($Fy$=36$ ksi$).$ New girder is

ASTM A$992$ steel $($Fy$=50$ksi. All columns are W$8$x$31.$ Use the LRFD Method.

Assumptions:

$1-$ The loads given include column and beam self weights.

$2-$ Existing beam and new girder are simply supported at both ends.

$3-$ New girder top flange is laterally braced at mid span and at girder ends only.

$4-$ Columns are continuous from foundation to roof and are prevented from sway at

floor level and at roof level in both directions.

$5-$ Columns are pin supported at foundation, at floor level, and at roof level.

Required:

$1-$ Find the lightest W$36$ girder that can be used to support the given loads. Limit the

new girder live load deflection to $\frac{1}{2}"$ maximum.

$2-$ Check the adequacy of the W$8$x$31$ column in the lower story at line $"$A$"$ for the

existing loads plus the new loads. Neglect the eccentricity of the reactions from

the new girder