Determine the thermal stress in the bar, Civil Engineering

Assignment Help:

Determine the thermal stress in the bar:

A stepped bar made of aluminum is held between two supports. The bar is 900 mm in length at 38ºC, 600 mm of which is having a diameter of 50 mm, while the rest is of 25 mm diameter. Determine the thermal stress in the bar at a temperature of 21ºC, if

(a) The supports are unyielding, and

(b) When the supports move towards each other by 0.1 mm.

Given E for aluminum = 74 kN/mm2

α for aluminum = 23.4 × 10-6 K-1

Solution

When the Supports are Unyielding

We have, L1 = 600 mm; diameter d1 = 50 mm

Thus,  A1 = π(50) 2/4 mm2

Also,   L2 = 300 mm; diameter d2 = 25 mm

Therefore, A2 = π(25) 2/4 mm2

and     ΔT = 38 - 21 = 17ºC

Therefore, free contraction, ΔL = L α ΔT = 900 × 23.4 × 10- 6 × 17 = 0.358 mm. Let σ1 be the stress in 50 mm φ part and σ2 be the stress in 25 mm φ part.

Then,

σ1 =   ΔTEA2 αL/A1L2 +A2L1 = 900 × 23.4 × 10 -6  × 17 × 74 × 103 × π × (25) 2/4(π × (50)2/4× 300 + π × (25) 2/4 × 600)

= 14.72 N/mm2

σ2 = σ1 (A1 + A2) =14.72 × (50) 2/ (25) 2= 58.88 N/mm2

These stresses are tensile in nature

When the Supports Move towards Each Other by 0.1 mm

Here,  ΔL´ = 0.1 mm.

∴          σ1 =   EA2 [ΔL - ΔL′]/ A1L2 + A2 L1 = 74 × 103 × π × (25) 2 × (0.358 - 0.1)/4(π × (50) 2/4 × 300 + π × (25) 2 /4× 600)

= 10.61 N/mm2

∴          σ2 = 10.61 × (50) 2/ (25) 2 = 42.44 N/mm2

Both these stresses are tensile.


Related Discussions:- Determine the thermal stress in the bar

What is gravity flow, Gravity flow is fluid flowing because of the forces o...

Gravity flow is fluid flowing because of the forces of gravity alone and not to an applied pressure head. In the Bernoulli equation, the pressure term is omitted, and the height an

Explain the routine inspections - inspection of bridge, Explain the Routine...

Explain the Routine inspections - inspection of bridge? These determine the physical and functional condition of the structure, identifying changes from the inventory, baseline

Define hand tools for underwater inspection of bridge, Define Hand Tools fo...

Define Hand Tools for Underwater Inspection of Bridge? Hand tools involve scrapers, wire brushes, chain and wire ropes. Tools of this kind are suited in which cleaning is confi

Functions of bedding below storm water drains, Question What are main funct...

Question What are main functions of bedding below storm water drains ? Answer Bedding that is normally made of granular resources or concrete serves four main functions as optio

Define the usage of data from hydrographs, Define the usage of Data from Hy...

Define the usage of Data from Hydrographs Flow rates and volume quantities over time. Predictions based on the runoff flow rates. The characteristics of the drainage b

Explain about warren truss, Q. Explain about Warren Truss? A truss is a...

Q. Explain about Warren Truss? A truss is a simple structure whose members are subject to axial compression and tension only and however not bending moment. The most common tru

Parallel pipe systems or multipath pipeline problems, Parallel Pipe Systems...

Parallel Pipe Systems or Multipath Pipeline Problems Two or more sections of piping (branches) of different diameters, lengths and/or pipe materials originating and terminating

Define underwater magnetic particle testing, Define Underwater Magnetic Par...

Define Underwater Magnetic Particle Testing? Underwater magnetic particle testing (UWMT) is a non-destructive testing suited for detection of surface cracks or discontinuities

Fracking, cons and pros of fracking

cons and pros of fracking

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