Calculate force required for equilibrium, Mechanical Engineering

Assignment Help:

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


Related Discussions:- Calculate force required for equilibrium

Explain about the footings how it is transmit loads, Explain about the foot...

Explain about the footings how it is transmit loads. Footings are generally the lowermost supporting part of the structure known as sub-structure and are the last structural e

Explain concept of radial drilling machine, Concept of Radial Drilling mach...

Concept of Radial Drilling machine Radial Drilling machine is a large gear headed drill press in which the head moves along the arm that radiates from the column of the machine

TIG welding, TUNGSTEN INERT GAS WELDING (TIG) In this process, an arc i...

TUNGSTEN INERT GAS WELDING (TIG) In this process, an arc is struck between a non consumable tungsten electrode and the base metal. The tungsten electrode is called non consumab

A solid sphere is rotating in free space, A solid sphere is rotating in fre...

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same  which one of the following will not be affected? Solution) In free space, nei

The parts and design of the pocket amp, The problem: - Deaf blind peop...

The problem: - Deaf blind people have a huge problem when crossing the streets. They always need assistance from a sighted person or a trained dog to cross the street. There i

Btec, advantages and disadvantages of kanban

advantages and disadvantages of kanban

Sada, Ask question #ccMinimum 100 words accepted#

Ask question #ccMinimum 100 words accepted#

#tittle thrumo , ES 347 - Thermodynamics Project Assigned: 3/28/2013 Due: 4...

ES 347 - Thermodynamics Project Assigned: 3/28/2013 Due: 4/25/2013 Problem specification 5 kg of air is contained in a piston-cylinder device, initially at a pressure of 2MPa and a

Laws of solid friction, Laws of solid friction: Sol.: The friction w...

Laws of solid friction: Sol.: The friction which exists between two surfaces that are not lubricated is called as solid friction. The two Surfaces can be at rest or one of t

Thermodynamics, What are significnces of quasi static process

What are significnces of quasi static process

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd