Determine change in length of the bar:

A steel bar is subjected to loads as shown the given figure. Determine change in length of the bar ABCD of 18 cm diameter. E = 180 kN/mm2.                                                                                                                      

Sol.:

As                           d = 180mm

E = 180 × 103  N/mm²

 

L_AB = 300mm

L_BC = 310mm

L_CD = 310mm

From the given figure

Load on portion AB = P_AB  = 50 × 103 N

Load on portion BC = P_BC  = 20 × 103  N

Load on portion CD = P_CD  = 60 × 103 N

Area of portion AB = Area of portion BC =  Area of portion CD = A = Πd²/4

=     (180)2/4 = 25446.9 mm²

By using relation   l = Pl/AE

δL_ab  = (50 × 103  × 300)/( 25446.9 × 180 × 103) = 0.0033mm ---------------- Compression

δL_bc  = (20 × 103  × 310)/( 25446.9 × 180 × 103) = 0.0012mm ---------------- Compression
δL_cd  = (60 × 103  × 310)/( 25446.9 × 180 × 103) = 0.0041mm ---------------- Compression
As net change in length  = -  δ L_ab  -  δ L_bc  - δ  L_cd

= - 0.0033 - 0.0012 - 0.0041

= - 0.00856 mm

Decrease in length = 0.00856mm                                                                        .......ANS

 

Posted Date: 10/23/2012 1:53:51 AM | Location : United States

Ask an Expert

Related Discussions:- Determine change in length of the bar, Assignment Help, Ask Question on Determine change in length of the bar, Get Answer, Expert's Help, Determine change in length of the bar Discussions

Write discussion on Determine change in length of the bar
Your posts are moderated

Write your message here..

Related Questions

Show hazards associated with plants, Q. Show Hazards associated with plants... Q. Show Hazards associated with plants? Hazards associated with plants will typically include the following: • Inherent fire hazards presented by the release of flammable g

Tool geometry, why single point cutting tool used in lathe why single point cutting tool used in lathe

Theorem of parallel axis, Theore m of parallel axis It states that if ... Theore m of parallel axis It states that if the M.I. of plane area about the axis passing through the C . G . can be denoted by I G . The M . I . of area about any other

Group technology, what is the gt? what is the gt?

Find out dimension of the cross section of the beam, Q.  A wooden beam of t... Q.  A wooden beam of the rectangular cross section is subjected to bending moment of 5KNm. If the depth of section is to be double the breadth and stress in wood is not to exceed 6

Megger, assignment assignment

Three particle system, Three Particle System Suppose we have two partic... Three Particle System Suppose we have two particles of masses  m 1  and  m 2   already fixed in space at distance  r 12  from each other. Let us bring in a third particle of

Communication , is effective communication an integral aspect in the mechan... is effective communication an integral aspect in the mechanical engineering field?

Thermodynamics, describe equivalence of kelvin planck and clausious stateme... describe equivalence of kelvin planck and clausious statement

Pultrusion, Pultrusion Structure sections of long length are generated... Pultrusion Structure sections of long length are generated by putting the fibres via resin bath and heated dies of exact shapes. Unidirectional fibres along with high volume f