A 9-m length of 6-mm-diameter steel wire is to be used in a hanger. The wire stretches 18mm when a tensile force P is applied. If E = 200 GPa, determine the magnitude of the force P, and the normal stress in the wire.

The magnitude of the force is 11.3KN and the normal stress is 400 MPa

Given that length (L) = 9 m, diameter (d) = 6 mm = 6 * 10⁻³ m, extension (δ) = 18 mm = 18 * 10⁻³ m, E = 200 GPa = 200 * 10⁹ Pa

The area of the wire (A) is:

The magnitude of the force is 11.3KN and the normal stress is 400 MPa

link

Force P is 11304 N and normal stress is 400 N/mm²

Explanation:

Given-

Length, l = 9 m = 9000 mm

Diameter, d = 6 mm

Radius, r = 3 mm

Stretched length, Δl= 18 mm

Modulus of elasticity, E = 200 GPa = 200 X 10³MPa

Force, P = ?

According to Hooke's law,

Stress is directly proportional to strain.

So,

σ ∝ ε

σ = E ε

Where, E is the modulus of elasticity

We know,

ε = Δl / l

So,

σ = E X Δl/l

σ =

We know,

σ = P/A

And A = π (r)²

σ = P / π (r)²

Therefore, Force P is 11304 N and normal stress is 400 N/mm²

answer:

design model: consists of design geometry; can be 2d or 3d; typically has a black background.

design files: drawing created with microsoft expression design, a drawing and design program for windows; may contain both vector and raster graphics; can also include multiple layers and various image effects.

elements: an element is a single part of a larger group.