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

Energy absorbed in heeling during vessel berthing, Q. Energy absorbed in he...

Q. Energy absorbed in heeling during vessel berthing? When a vessel   berths on a fender system at a pier, point of contact of berthing ship can be below or above the centre of

Distomat, definition,old&new modern&difference

definition,old&new modern&difference

Material which can endures vibrations and saline conditions, material which...

material which can endures vibrations and saline conditions

Determine the ultimate bearing capacity of a square footing, Determine the ...

Determine the ultimate bearing capacity of a square footing, 1 m × 1 m, resting on saturated clay of unconfined compression strength of 180 kN/m 3 and a bulk density of 18 kN/m 3

Types of limes and their properties, Types of Limes and their Properties ...

Types of Limes and their Properties The limes are classified in three categories as fat lime, hydraulic lime and poor lime: (1) Fat lime: It is composed of 95 percentage o

Earth dam, earth dam design and its force

earth dam design and its force

Water waste engineering, wahat is physical characteristic on total suspende...

wahat is physical characteristic on total suspended solid

Material of steel tendons, Material of steel tendons The material of s...

Material of steel tendons The material of steel tendons also must be of a high strength. Tendons should possess required material and geometrical properties so that a desired

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