Your consulting engineering firm has been approached by a client to evaluate a roof design for a small warehouse. The primary design being considered is composed of Pratt roof trusses that are uniformly spaced at $5\mathrm{.}5m$ centers and the span of the truss is $15m.$ The height at the peak is $6\mathrm{.}0m$ from the bottom cord. A typical drawing for a truss is shown in Figure $1.$ In addition to evaluating this proposed design, your design team must propose a second alternative solution. Your design should have different number of equal width panels and a different truss type $($not a Pratt truss$).$ The building is located on an industrial estate in the city of Durban. A huge part of the surface in the area is covered with buildings.

rigure $1$: vesign option $1($rratt truss$)$

Additional information:

Length of the structure $=50000mm$ Trusses are spaced $5500mm$ apart

Height at eaves $=10000mm$

There are two $35004000mm$ high shutter doors on one gable wall of the structure.

Roof truss and loading information:

Purlins are spaced at $2500mm$ measured horizontally $($At joints in the top chord of the truss$).$

Purlins: $1807022k\frac{g}{m}$ channel sections.

Bottom chord: $25414631k\frac{g}{m}$ I sections.

Top chord and bracing members: $15015015k\frac{g}{?}$ angle sections.

Roof sheeting : $0\mathrm{.}8mm$ thick IBR sheeting

Thermal insulation: panels with a mass of $1\mathrm{.}20k\frac{g}{m^2}$

Services: sprinkler system and lighting system with a mass of of $6\mathrm{.}5k\frac{g}{m^2}.$

Assume the mass of each truss to be approximately $15k\frac{g}{m^2}.$

An aluminium signage board with dimensions $2\mathrm{.}5m$ high $6\mathrm{.}0m$ wide $0\mathrm{.}025m$ thick hangs centrally $($Joint L$2$ and L$4)$ on the bottom chord of the truss. Allow an extra $50kg$ for lighting equipment and fixings.

For live$/$imposed loading, find the relevant extracts from the South African Standard $($SANS $10160-2$:$2011.$ The roof structure will be accessible for maintanance and repairs.

Truss loading, support and member connectivity information:

The loading on the structure comprises the following components:

Truss self$-$weight $($dead load$)$

Signage weight $($dead load$)$

Live load

Wind loading

The truss has bolted connections to the supporting load bearing walls. However, the connection on the right side is designed to allow horizontal translation to occur at that joint. The purlins are angled along the top members of the truss and are connected such that both horizontal and vertical force components can be transferred to the truss. Once all these individual loading components have been found, they are to be combined and applied to a typical internal frame according to where they physically act in order to determine the maximum ultimate limit state load. Please note, consider the self$-$weight of the truss, and any live loading to act as a uniformly distributed load along the truss span $(k\frac{N}{m}),$ which will be 'idealised' as equivalent point loads acting at the truss joints, when carrying out your analysis.

Design tasks:

a$)$ For the truss in Figure $1$ above, discuss its determinancy and stability, both internal and external. Show relevant calculations and explain your reasoning.

b$)$ Determine the design loading on a typical internal purlin and draw the bending moment diagram to obtain the maximum design moment.