The wires each have a diameter of 12 mm, length of 0.6 m, and are made from 304 stainless steel. Determine the magnitude of force P so that the rigid beam tilts 0.015∘.

Magnitude of force P = 25715.1517 N

Explanation:

Given - The wires each have a diameter of 12 mm, length of 0.6 m, and are made from 304 stainless steel.

To find - Determine the magnitude of force P so that the rigid beam tilts 0.015∘.

Proof -

Given that,

Diameter = 12 mm = 0.012 m

Length = 0.6 m

= 0.015°

Youngs modulus of elasticity of 34 stainless steel is 193 GPa

Now,

By applying the conditions of equilibrium, we have

∑fₓ = 0, ∑ = 0, ∑M = 0

If ∑ = 0

⇒×0.9 - P × 0.6 = 0

⇒×3 - P × 2 = 0

⇒ =

If ∑ = 0

⇒×0.9 = P × 0.3

⇒ ×3 = P

⇒ =

Now,

Area, A = = 1.3097 × 10⁻⁴ m²

We know that,

Change in Length , =

Now,

= 9.1626 × 10⁻⁹ P

= 1.83253 × 10⁻⁸ P

Given that,

= 0.015°

⇒ = 2.618 × 10⁻⁴ rad

So,

⇒2.618 × 10⁻⁴ = (  1.83253 × 10⁻⁸ P - 9.1626 × 10⁻⁹ P) / 0.9

⇒P = 25715.1517 N

∴ we get

Magnitude of force P = 25715.1517 N

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