Design of a Signpost

PART A

Introduction

Structural elements, machine parts etc. are frequently subjected to combined loading. The signpost is a classic example which involves axial loading, bending, torsion and transverse shear.

Purpose

The purpose of this project is to assist you master relevant principles studied in the course.

PART B

Task

Determine the most economical square, rectangular or circular Grade $350$ steel tube section $($SHS$,$ RHS or CHS$)$ to support a cantilevered roadside sign similar to the one at the service station on the corner of Parkland Dr and Engineering Dr$,$ Southport. Assume the cost per kg is constant, i$.$e$.$ the lightest section is the most economical. For the sake of simplicity, you are required to first choose the tube section $($SHS$,$ RHS or CHS$)$ based on the normal stress $($e$.$g$.$ you must ensure that the maximum normal stress caused by the external loads does not exceed the allowable normal stress$).$ After obtaining the suitable tube section, you must also check the shear stress by torsion and transverse shear force $($e$.$g$.$ you must ensure that the maximum shear stress on the chosen section does not exceed the allowable shear stress$).$

Design Data

Dimensions:

The bottom of the sign is to be $4$ m above ground level and the top is to be $6$ m above It is to be $3$ m wide, from the side of the column.

Loads

Sign dead weight $=($X$/10+5)$ kN$,$ where X is the last two digits of your student numbers. For instance, if the student number is $1234567,$ then the load is $67/10+5=11\mathrm{.}7$ kN$.$ This load will act at a distance of $5$ m out from the edge of the column, so it will have $2$load effects$$: an axial compressive load and a bending moment.

Self$-$weight of colum You will not know this until you choose a section, but you can assume a weight for a start and adjust it later.

Wind load: assume $($Y$/30)$ kPa normal to sign and on column, where Y is the first two digits of your student numbers. For instance, if the student number is $1234567,$ the wind pressure is $12/30=0\mathrm{.}4$ kPa. You will not know the exact area of the column until you determine the section, so assume a reasonable value for a start, and then adjust it later if necessa The wind load will have $3$ load effects on the column:

$($i$)$ bending moment

$($ii$)$ torque

$($iii$)$ transverse shear force.

Available material

o Tables of sections available from the Appendix or websites $($see below$).$

o The steel is Grade $350,$ i$.$e$.$ guaranteed minimum yield stress, $\backslash$sigma y$,$ is $350$ MPa;

o An allowable normal stress, $\backslash$sigma all, of $2/3$ of the yield stress, as a factor of safety of $1\mathrm{.}5$ is taken against yield; and

o An allowable shear stress, $\backslash$tau y$,$ of $1/3$ of the yield stress.

project $2$ figure $1-1.$png

Figure $1.$ Typical sign$-$post dimensions $($dimensions not scaled$).$

PART C

Submission of the Design

$5$ PM Friday $($Week $12),$ online submission

Report Format and Presentation

Requirements

The assignment could be typed, but use plenty of diagrams and refer to them to explain and demonstrate.

Individual, not team work. Weighting $10\%.$

Important notes

Presentation.

Use just enough words to make clear your train of thought. Use plenty of simple diagrams $($they can be freehand$),$ drawn approximately to scale so it $$looks right$,$ to make clear what dimensions you are referring to$.$ For example $$Length $=27$ mm$$ means nothing. Length of what? The reader can$$t read your mind. But $$length L $($Figure $2)=27$ mm$$ is fine. As long as your reader can find Figure $2.$

Technical details

Sketch the structure and mark in the loads.

Think about where the critical cross$-$section will be$.$

Mark in an x$-$axis along the ground below the sign, y$-$axis up the centre of the column, and a z$-$axis along the ground at right angles to the sign.

Assume a cross$-$section $($e$.$g$.150\backslash$times $150\backslash$times $5$ SHS$).$

Calculate axial load P$,$ transverse shear force V$,$ torque Ty about the y axis and moments Mx$,$ Mz about the x and z axes respectively.

Calculate stresses on the critical section due to each of these load effects.

If the stress is too high, choose a larger cross If the stress is too low the chosen section is not economical, so choose a smaller section. You may like to do this as a spreadsheet or use Matlab. Once you set up the basic equations it is then easy to check other sections.

You should check all $3$ section types: CHS$,$ SHS$,$ and RHS$.$ It is not obvious which will give you the lightest design. You should find one that works and show that the next size down fails, so you have the most economical section.

Your report should show calculations clearly so they can be easily checked, and it should be clear which section you have chosen, and why.

The first moment of area for the highlighted arc $($see Figure $1)$ is given as:

Q $=(2/3)($ro$3$ ri$3)$sin$\backslash$alpha

where ro is the outer radius, ri is the inner radius, and $\backslash$alpha is the angle as shown in Figure $1.$

project $2$ figure $1.$png

Figure $1.$ Circular hollow sectionFigure $1.$ Typical sign$-$post dimensions $($dimensions not scaled$).$