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
A copper bar 80 mm by 60 mm in cross-section (k = 370 W/m ºC) is lying in a insulated trough so that the heat transfer from one face both the edges is negligible. It is seen that w

Effective communication is an itergral aspect in the mechanical engineering field, base on arguement

What are the objectives of the earth pressure and retaining structures? After knowing all concepts about the same you should be able to learn: a. Know the field situations w

what is the velocity and acceleration when connecting rod and crank are mutually perpendicular?

Define different regimes of boiling and depict their ranges on a excess temperature curve us heat flux. Also distinguish between laminar film condensation and dropwise condensation

Evaluate the motion of the system: If in above Example, the block A is resting on an inclined plane at 45 o to horizontal as illustrative in Figure, find out the motion of th

Difference between SI and CI engines SI engine stands for spark ignition engine while CI engine stands for compression ignition engine. SI engine works on the principle of w

brief description of resonant cavities

STORAGE AND HANDLING OF ELECTRODES It is recommended that the electrodes should be stored in a warm and dry place. Generally, conditions of storage in the shop are not very condu

Types of Splitwedge gate arrangement need to understand