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


Q. Show Application to Gyroscope? A fiber optic Gyroscope is used to detect the mechanical rotation of the interference of light. Two beams travel along the fiver in opposite d

explain capacity planning system

Types Of Polymerisation When some of bifunctional molecules connect in a chain structure, the reaction is termed as addition polymerisation.  However, these polymerizations do

Differences between torque and torsion: Give differences between torque and torsion. List a few examples of torsion in the engineering practice. Sol.: When structural or

In an orthogonal cutting test with a tool of rake angle 10 degree , the following observations were made. 20 Chip thickness ratio = 0.3 Width of cut = 6mm Uncut chip thicknes

when is scaling transformation termed as linear

a) You have been assigned to design a robotics spot welding experiment for low carbon steel sheets. You found an experimental power source for spot welding process which is designe

What is Floating Foundations The settlement of  foundations can be reduced if the applied load is compensated by excavation of a basement. This basement may be in the form of