Q6 (1 mark) Lightweight display stand

The figure below shows a concept for a lightweight display stand (a column under compressive

loading). The column must support a mass m of 300 kg, to be placed on its upper surface at a

height h, without failing by elastic bucking. It is to be made of a tube and must be as light as

possible.

1) Derive the material index for the tubular material of the stand that include the shape of

the section, described by the shape factor

12/

A²

where A is the section area of the column. Table 1a summarizes the requirements.

Table 2 design requirement for stiff and light hemispherical shell

Load F = mg

Function

Constraints

Objectives

Free variables

• Light weight Column

• Specified buckling load F

•

Height h specified

Minimize mass m

Choice of material

Sectional shape

Cross-sectional area A

•

•

at

2) Use the four-quadrant chart to work out if it is possible to replace a stand that is

currently an Al-alloy tube with a timber column with the same performance (hint: same

kilogram per unit length, kg/m). The detail of the cross-sectional shape of the Al-alloy

tube is given in Table 3. Note that the shape of the timber column can vary. However,

the maximum shape factor for timber is 8 (hint: if the required shape factor for

timber is less than 8, then the substitution is possible./nMECH3301 Materials Selection, Tutorial 3

Materials

Al-alloy

Ashby MSMS, 4 & 5 EDS.

Table 3 shape of the Al-alloy tube

Shapes

O

"↑

Shape specification

r

»t;/=

-=

r»t;

= 20

MY Lu, 2023