Calculate force required for equilibrium:

A member ABCD is subjected to the point loads P₁, P₂, P₃  and P₄  as shown in the figure given below

Calculate force P₃ required for equilibrium if P₁ = 120 kN, P₂ = 220 kN and P₄ = 160 kN. Determine the net change in length of member. Take E = 200 GN/m².
Sol.: Modulus of elasticity E = 200 GN/ m² = 2 × 10⁵ N/mm².

By considering equilibrium of forces along axis of the member.

P₁ + P₃ = P₂ + P₄;

120 + P₃ = 220 + 160

Force P₃ = 220 + 160 - 120 = 260 kN

The forces which are acting on each segment of member are shown in free body diagrams shown below:

Let  δL₁,  δL₂ and  δL₃,  be extensions in parts 1, 2 and 3 of steel bar respectively. Then,

 

 
As, Tension in AB and CD but compression in BC,
So, Total extension of the bar,
    
Extension of segment AB = [(120 × 10³) × (0.75 × 10³)]/[1600 × (2 × 10⁵)] = 0.28125 mm

Compression of segment BC = [(100 ×10³) × (1 × 10³)]/[625 × (2 × 10⁵)] = 0.8 mm

Extension of segment CD = [(160 ×103) × (1.2 × 10³)]/[900 × (2 × 10⁵)] = 1.0667 mm

Net change in length of the member = δl =0.28125 - 0.8 + 1.0667 = 0.54795 mm (increase)        .......ANS

Posted Date: 10/23/2012 1:45:59 AM | Location : United States

Ask an Expert

Related Discussions:- Calculate force required for equilibrium, Assignment Help, Ask Question on Calculate force required for equilibrium, Get Answer, Expert's Help, Calculate force required for equilibrium Discussions

Write discussion on Calculate force required for equilibrium
Your posts are moderated

Write your message here..

Related Questions

Modulus of elasticity, Explain Young's Modulus or Modulus of elasticity? ... Explain Young's Modulus or Modulus of elasticity? Sol. : It is ratio between tensile stress and tensile strain or compressive stress and compressive strain. It can be denote

Find out the moment of inertia of a semicircle, Find out the moment of ine... Find out the moment of inertia  of a semicircle: Find out the M. I. of a semicircle ABM around its periphery AB and also around centroidal axes x and y as illustrated in Figur

Illustrate volumetric efficiency of a compressor, Illustrate what is meant ... Illustrate what is meant by volumetric efficiency of a compressor ? Illustrate how clearance volume affects it. Discuss the effects of clearance volume on the performance of an air

Pulleys, what do you mean by law of belting and also explain the crowning o... what do you mean by law of belting and also explain the crowning of pulleys ?

External pressure design of unfired pressure vessels, Q. External Pressure ... Q. External Pressure Design of unfired pressure vessels? Determine requirements for external pressure based on the expected operation of the vessel, and add a suitable operatin

Laser beam welding, LASER BEAM WELDING In this process, fusion is ac... LASER BEAM WELDING In this process, fusion is achieved by directing a highly concentrated beam to a fine spot. The word LASER  is an abbreviation of Light Amplification by S

Vibration, steady state amplitude steady state amplitude

Machine elements, instant center of direct contact slider instant center of direct contact slider

Mechanics of solid, determine crippling load for T section dims 12cm??12cm?... determine crippling load for T section dims 12cm??12cm??2m and of length 6m it used as colum with one of its end fixed and other hinged E=2??10 power 5 N/mm2

Engine lubrication system , Engine Lubrication System: This system facilit... Engine Lubrication System: This system facilitates the lubrication of all the engine components, gears and other associated parts.