DESIGN SHORT $3-$ INDETERMINATE STRUCTURAL ANALYSIS AND STEEL STRUT

DESIGN

The land owner $($introduced in Design Short $2)$ is planning on significant renovations to part of their estate and they wish to use the reinstated bridge as access for construction plant and materials. The variable load capacity of the beams you identified in Design Short $2$ is significantly lower than that required for the new intended use of the bridge. The land owner has suggested placing steel struts under the mid$-$point of each beam of each span to enhance their variable load carrying capacity. Using LUSAS and the design guidance provided in Design Short $2$ determine the maximum variable load $($per $m^2)$ that the deck can now support, based on the capacity of the beams in bending and shear. You are also asked to design the steel struts $($HINT: try the smallest universal column section first$).$ For this you will need to apply the appropriate ULS partial factors to the permanent and variable loads. Please provide full calculations to support your answers.

You may assume the following;

The $125mm$ thick deck plate is formed from timber and has the capacity to withstand a greater variable load than the beams;

The beams are continuous over pinned supports;

The struts are partially restrained in direction at both ends.

The elevation and cross section of the bridge structure are shown below $($Figures DS$3\mathrm{.}1$ and DS$3\mathrm{.}2)$ together with the beam dimensions $($Figure DS$3\mathrm{.}3).$ All dimensions are in $mm.$

Figure DS$3\mathrm{.}2$ Cross section through bridge structure

DESIGN DATA

Plastic Lumber Beams

Elastic $($short term$)$ modulus $,=2\mathrm{.}4$GPa

Density, ${}_{\text{b}\text{e}\text{a}\text{m}\text{s}},=8\mathrm{.}7k\frac{N}{m^3}$

Flexural Strength, ${}_y$

Shear Strength, ${}_v$

Figure DS$3\mathrm{.}3$ I beam dimensions

Timber deck plate

Density, ${}_{\text{d}\text{e}\text{c}\text{k}}=8k\frac{N}{m^3}$

Note: The strengths are serviceability stress limits$,$ therefore you undertake the calculations with serviceability load

factors $($i$.$e$.$ partial factors $=1\mathrm{.}0)$

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