Bending Deflection at Home Experiment

OBJECTIVE:

Study the deflection behaviour of Beams.

APPARATUS:

Choose any material of your choice which can show deflection under loads

Any instrument to help you measure with

Home made weights$($various Weights to show different deflections, but be careful not to break your beam$)-$ plan carefully as to increase the weights etc

Build home made simple supports for your beam

METHOD:

Measure the width $(b)$ and$/$or depth $(d)$ and or diameter $()$ of each beam $($Table $1)$ depending on what cross$-$sections you choose. Adjust the following tables according to your cross sections. At least $3$ beams with varying cross sections.

For your various beams, determine the center and the deflection for central point with different loads according to Part A$,$ B and C$.$ Repeat for $10$ different values of loads.

Use the Tables $1,2,3$ and $4$ to help you tabulate your results clearly as instructed in Part A$,$ B and C $.$

Part A$.$

$3.$ For a given central point load determine the central deflection $()$ of one beam $($Repeat for ten different values of loads. $($Column $1$&$4,$ Table $4)$

Part B$.$

$4.$ For given central point load determine the central deflection to five different spans $,L_4,L$ s$)$ of one beam $($move the supports one step each towards the center$)($Table $2)$

Part C$.$

$5.$ For various beams, using a constant span and central point load, determine the central deflection $($as in $3$ but $L$ is of your choice.$)($Table $3)$

ANALYSIS AND REPORT

Graphs:

Plot $W$ against $$ for L constant for step $3$

Plot $logL$ against $log$ for $W$ constant for step $4$

Plot $logd$ against $log$ for constant $W$ and $L$ for step $5$

Determine $E$ young's modulus from graphs $1,2$ and $3$

Conclusions:

Write down the conclusions briefly, and comment on the different values of E calculated above the values of deflection measured in step $7$ in relation to the superposition principles and reciprocal theorem.