Calculate force required for equilibrium, Mechanical Engineering

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

700_Calculate force required for equilibrium.png

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,

 

845_Calculate force required for equilibrium1.png 
As, Tension in AB and CD but compression in BC,
So, Total extension of the bar,
   1318_Calculate force required for equilibrium2.png 
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







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
Related Questions
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 M. I. of a semicircle ABM around its periphery AB and also around centroidal axes x and y as illustrated in Figur

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

what do you mean by law of belting and also explain the crowning of pulleys ?

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 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

steady state amplitude

instant center of direct contact slider

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