Assignment Activity and Guidance

Task $1$

$($a$)$ A simply supported beam is used as the main support for the floor of a mast climbing platform and is subjected to the loads given below.

The designers wish to visualise how the position of loads within the working platform impact upon the moments experienced by the beam. Derive the expressions for the bending moments in the heam, and hence produce a graph showing the bending moment distribution along the length of the beam.

The beam selected has a rectangular cross$-$section with a height of $50$ mm and a width of $40$ mm $.$ Determine the maximum stress on the surface at the point of the beam where the highest bending moment occurs so that the design team can establish if any cost and weight savings can be made.

$($b$)$ The transverse support member within the same platform can be considered to be a simply supported beam and is$.$subjected to the loads given below. You have been tasked with amending the design and making weight savings wherever possible.

To allow your work to be checked by a colleague you are asked to produce a fully labelled sketch of the shear force distribution along the length of the beam.

As part of this analysis you have been asked to derive the expressions for the bending moments in the beam, and hence produce a graph showing the bending moment distribution along the length of the beam.

Given that the maximum allowable tensile stress in the beam is $350$ MPa $,$ determine the lightest possible section to use for this structure, using a universal beam to BS $4$ part $1$:$2005.$ Ensure that the relevant section of the steel stock table is presented with your answer, clearly indicating and justifying the beam you have selected.

$($c$)$ A cantilever beam representing a wall tie rod for a construction hoist is shown below. To allow appropriate wall fixings to be designed by another engineer, determine the maximum shear force and bending moment in the beam if the beam is $2$ m long and a $4$ kN point load is applied as shown.

$($d$)$ Repeat this analysis for the beam, assuming that the point load is replaced with a uniformly distributed load of $2k\frac{N}{m}$ that extends along the full length of the beam.

$($e$)$ A $2$ m long encastr$$ beam is given below and represents part of the base frame of the platform. To allow a colleague to design appropriate weld joints to secure the beam in place determine the maximum shear force and bending moment if a load of $4$ kN is applied halfway between the end supports, as shown.

$($f$)$ To allow different design cases to be examined, repeat this analysis for the beam shown above, but with the point load replaced with a uniformly distributed load of $2k\frac{N}{m}$ that acts along the entire length of the beam.