PLEASE ONLY SOLVE ANALYSIS QUESTIONS AND LOAD CASES USING THE DESIGN DATA AND ASSUMPTIONS GIVEN BELOW:

The owner of a building complex has planned to infill the space between two existing adjacent buildings with

a new multi$-$bay single storey building and roof garden. The new $30-$metre long structure will comprise frames

at $5$m centres that support a pre$-$cast concrete roof deck. A cross$-$section through one of the internal frames

is shown in Figure $4\mathrm{.}1.$ The variable load to be supported by the roof deck has been calculated to allow for a garden area and a set of light$-$weight free$-$standing structures. You are required to design both an internal concrete frame and a steel frame to support the roof structure and associated loads, assuming that both frames are continuous structures.

You should use the stiffness$-$based matrix method.

You should assume the following:

The roof deck comprises $250$ thick precast concrete units that span between the frames, overlaid with

a $50$mm mortar screed. The total characteristic permanent load of the units and screed is $5$k$($N$)/($m$^(2)).$

The characteristic variable load is $7\mathrm{.}5$k$($N$)/($m$^(2)).$

The beams are pinned at their intersection with the existing buildings.

The existing buildings have structural elements capable of supporting the beam loads at the necessary locations.

The columns are supported by an existing raft foundation located $1000$mm below the finished floor level $($FFL$)$ of the new structure.

There are pinned supports at the base of the columns.

The beam$-$column connections should be considered continuous $($i$.$e moment carrying$).$

DESIGN DATA:

Concrete frame

${}_{\text{c}\text{o}\text{n}\text{c}}=25k\frac{N}{m^3},f_{ck}=40\frac{N}{m}{m}^2,f_{\text{c}\text{t}\text{e}\text{f}\text{f}}=3\mathrm{.}5\frac{N}{m}m2,f_{yk}=f_{ywk}500\frac{N}{m}{m}^2,$

$E_{cm}=35k\frac{N}{m}{m}^2,E_s=200k\frac{N}{m}{m}^2,$ cover $=30mm$

Steel frame

${}_{\text{s}\text{t}\text{e}\text{e}\text{l}}=78k\frac{N}{m^3},$ Steel $S275(Fe430)$

ANALYSIS:

The rotational stiffness $(\frac{M}{})$ of a pin$-$ended beam $=3E\frac{\text{I}}{L}$;

The rotational stiffness $(\frac{M}{})$ of a fixed$-$end beam $=4E\frac{\text{I}}{L}$;

The fixed end moment for a beam built$-$in at both ends $=w\frac{L^2}{12}$;

The fixed end moment at the built$-$in $($encastr$)$ end of a beam with a pin support at one end and an encastr$$ support at the other end $=w\frac{L^2}{8}$

You are not expected to redistribute moments.

Important: You will only need to solve a $22$ system of equations with the primary unknowns being the rotations at the two column$/$beam intersections.

Consider the following load cases for both frames;

i$.$ Ultimate permanent $+$ variable load across the entire length of the continuous beam.

ii$.$ Ultimate permanent $+$ variable load on the central span only and the unfactored

permanent load on the outer spans.

iii. Serviceability permanent $+$ variable load across the entire length of the continuous beam.

iv$.$ Serviceability permanent $+$ variable load on the central span only and the unfactored

permanent load on the outer spans.

v$.$ Quasi$-$permanent load across the entire length of the continuous beam.

vi$.$ Quasi permanent load on the central span only and the unfactored permanent load on the outer spans.