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

Neutral layer and neutral axis, Neutra l Layer and Neutral Axis In the...

Neutra l Layer and Neutral Axis In the beam or cantilever, there is one layer which retains the original length of it even after bending. So in this layer tensile stress and c

Define oxidation process, Q. Define Oxidation Process? Oxidation is def...

Q. Define Oxidation Process? Oxidation is defined as a loss of electrons, as when a metal goes from the metallic state to the corroded state. When a metal reacts with oxygen,

Strain, is strain in bending important parameter to consider?

is strain in bending important parameter to consider?

Supports for rigid bodies, Supports for Rigid Bodies: In this unit, yo...

Supports for Rigid Bodies: In this unit, you have learnt to classify various types of supports and constraints, rollers, rockers, ball and socket joints, cables, short links,

Thermal, Prove that energy is a property of system

Prove that energy is a property of system

Determine atomic packing factor, Determine APF of BCC and theoretical densi...

Determine APF of BCC and theoretical density in g/cm 3 , assuming the value of r=1.28A 0 and atomic weight is 60g/mol. Determine APF of FCC and theoretical density in g/cm 3 ,

Potential energy and kinetic energy- thermodynamics, Potential energy (PE) ...

Potential energy (PE) The energy possessed by body or system by virtue of its position above the datum level. The work done is because of its falling on earth's surface. Po

What is the function of a spark plug?, (a) What is the function of a spark ...

(a) What is the function of a spark plug? (b) What are the types of spark plugs? Point out the differences between them. (c) Describe the construction of a spark plug with th

Governor, what is the formula of sensitivity of governor?

what is the formula of sensitivity of governor?

Transformer for flash butt welding, Transformer for flash butt welding ...

Transformer for flash butt welding The transformer required for flash butt welding is similar to that needed for other resistance welding processes. Here, the transformer is to

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