Determine the thermal stress in the bar, Civil Engineering

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.

Posted Date: 1/30/2013 5:57:51 AM | Location : United States







Related Discussions:- Determine the thermal stress in the bar, Assignment Help, Ask Question on Determine the thermal stress in the bar, Get Answer, Expert's Help, Determine the thermal stress in the bar Discussions

Write discussion on Determine the thermal stress in the bar
Your posts are moderated
Related Questions
The inner diameters of a sampling tube and that of a cutting edge are 70 mm and 68 mm correspondingly, their outer diameters are 72 and 74 mm respectively. Verify the inside cle

Explain RCRA and HSWA - Hazardous Waste Regulations 1. In 1976, Congress passed the Resource Conservation and Recovery Act (RCRA) and directed EPA to establish hazardous waste

Enumerate the term - superposing the stress variations If the case of concentric pre-stressing is considered, we can appreciate that stress at any section of the beam is compr

Explain is Vadose Zone - Ground water In an unconfined aquifer, it is the area located above the water table and aquifer, where the soil and rock are not saturated with water.

Design of Flexible Pavements: The design of flexible pavements is done by the CBR method. The CBR test, described further, gives an indication of the supporting power of the

Define Carbonation - underwater inspection of bridge? Carbon dioxide is present in the air and attacks the concrete directly. It has the effect of destroying the normal passivi

3-d figure of line ranger

Q. Granite Tiles for construction material? At every important station for public urinals granite may be used as wall cladding drain and foot rest material. The water sinks at

Question What is designing level of landings in piers? Answer Landings are designed as resting place for passengers throughout berthing and deserting of vessels. I

State the Short Term Effects of concrete These are various types of effects produced, nearly instantaneously, due to the application of external loads on structures. An example