Stress-Strain problem and solution

Stress-Strain Problems and solutions:

A wire of length 2.50 m has a per-

centage strain of 0.012% when loaded with a tensile force. Determine the extension of the wire.

Solution:

Original length of wire = 2.50 m = 2500 mm

and strain = 0.012

100 = 0.00012

Strain ε = extension/originallength =x/L,

extension x = εL = (0.00012)(2500) = 0.30 mm

2) (i) A rectangular section metal bar

has a width of 10 mm and can support a maximum

compressive stress of 20 MPa; determine the

minimum breadth of the bar when loaded with a

force of 3 kN.

 (ii) If the bar in (a) is 2 m long and

decreases in length by 0.25 mm when the force is

applied, determine the strain and the percentage

strain.

(i) Since stress, σ = force/area

=F/ σ

then, area, A = 6

               = 3000 N/20×10^6 Pa

        = 150 × 10^–6 m2 = 150 mm2

Cross-sectional area = width × breadth, hence

 breadth = area 150

width 10 = = 15 mm

(b) Strain, ε = contraction 0.25

original length 2000 = = 0.000125

Percentage strain = 0.000125 × 100 = 0.0125%

3). A bar 1.60 m long contracts axially

by 0.1 mm when a compressive load is applied to

it. Determine the strain and the percentage strain.

Strain ε = contraction/original length

               =0.1mm/1.60×10^3mm

                =0.1/1600

                  =0.000625

Percentage strain = 0.0000625 × 100 = 0.00625%

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