Question

A steel wire ABC 16 m long having cross sectional area of 4 mm2 weighs 20 N as shown in figure 1.1. If the modulus of elasticity for the wire material is 200 GPa, find the deflections at points C ad D.

Answer 1

Solution;

Given;

P=20N

A=4mm²

L=16m

E=200GPa

Delfection of a cantilever is by;

$\delta=\frac{PL^3}{8EI}$

Since cross section is a square;

$A=s^2=4mm^2$

Therefore;

$s=2mm$

We can calculate I as;

$I=\frac{s^4}{12}=\frac{2^4}{12}=1.33mm^4$

Deflection at C;

$\delta_C=\frac{20×16^3}{8×200×10^9×1.33×10^{-12}}$ =38409.6m

Deflection at B;

$\delta_B=\frac{10×8^3}{8×200×10^9×1.33×10^{-12}}$ =2406.01m