stress strain basic-1

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Don’t blindly depends only on the

class notes, refer Text Book also.

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Hook’s Law 

• With in the elastic limit, the

applied stress(σ) is directly

proportional to strain (ε).• The proportionality constant is

called “Young’s Modulus”

(E or Y)

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TOUGHNESS: Energy absorbed

before failure; area under the curve

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Type-1

Calculations to find the change in

length

Simple Cases

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Formula to find the change in length

• P = Applied Load

• L = Length of the section in which the

change in length will be calculated

•  A = Area normal to the direction of the

application of the load

• E = Young’s Modulus 

 E  A LPl

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Category I

 A = 1000 mm2,

E = 1.05 x 10e5 N/mm2

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 ΔL = ΔL  AB + ΔL BC + ΔL CD

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Finding the unknown force

Category II

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Category III

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Recall: Formula to find the change in length

• P = Applied Load• L = Length of the section in which the

change in length will be calculated

•  A = Area normal to the direction of theapplication of the load

• E = Young’s Modulus 

 E  A LPl

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Category V

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Category VI

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Category VII

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Category VIII

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Category IX

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ELONGATION OF

THE BAR DUE

TO IT’S SELFWEIGHT

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Extension of taper rod/bar 

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Elongation of Circular Taper Bar 

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Problems

1) If a tension test bar is found to be taper from(D + a) mm diameter to (D – a) mm diameter,prove that the error involved in using the meandiameter to calculate the Young’s Modulus is

percent.

2) The bar A having width 4 mm through out itslength and thickness is 2 mm. The bar B

having constant thickness 2 mm but the widthtaper from 6 mm to 2 mm for a axial tensileload P. If both the bar elongate equally,determine the ratio of their length assumingboth bars are made of same material.

210

 D

a

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ELONGATION OF TAPER BAR

b

a

ba Et 

PL L elog

)(

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BAR OF UNIFORM STRENGTH

  L

 A

 A

2

1log

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BARS OF COMPOSITE SECTION

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Category composite

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THREE BAR SYSTEM

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Equivalent Area of Compound

Section

c

c

 E  E 

s

scs m  

C 

S 

 E 

 E 

m

Let A = Gross area of the column As = Area of the Steel

 Ac = Net area of concrete = (A – As)

σs and σc are the stress in Steel

and Concrete

Strain in Steel = Strain in Concrete

or,

Where called “Modular Ratio” Total Load on column = Load taken by steel rods + Load taken by concrete

P A A ccss   es

c A

P

 Am A

P

)1( 

 Ae = Equivalent area of Concrete

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TEMPERATURE STRESS

t lT T ll i f     )(

l = Length of the bar at the room temperature   Δl = Change in length 

 = coefficient of thermal expansion in per oC.Ti = Initial temperature of the body  Tf = Final temperature of the body  

 ΔT = Change in temperature 

If temperature deformation is permitted to occur freely, no load or stress will be induced in the structure. If the deformation due to the

change of temperature is prevented then, an internal stress is

induced. The internal stress is termed as thermal stress.

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http://www.mathalino.com/reviewer/mechanics-and-strength-of-

materials/thermal-stress

T  L

T  L

 L

ltemp

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 L

T  L

 L

ltemp

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Problem:1

Diameter of steel rod= 15 mm

Diameter of Copper rod =

40 mm I. D. And 50 mm O. D.Rise of Temp. is 60 degree

Calculate the stress developed in

each2

5

2

5 1005.1;101.2mm

 N  E 

mm

 N  E  cs

sccs C  per C  per       ;105.17;1012 0606

Problem:2

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Problem:2 T  L C   

T  L S   

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Video Lecture Series – 1

• Introduction to Strength of Materials

• By Prof. S. K. Bhattacharya, IIT Kgp.• Sunday 6.15 p.m. to 7.15 p.m. at

CDMM 404

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QUIZ-I

10 marks,

Objective Type•24TH Jan 10 MONDAY

•S. Q.- Ganga Xerox

137 138 & 139

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Extra Class

26TH JAN 2011

 Attendance will be taken

• 11.00 A.M. to 1.00 P.M. for E1/E2 and

• 3.00 P.M. to 5.00 P.M. E2/E1

Doubt Clearing Class

Second and Fourth Saturday of every month at GDN 131; 11.00 A.M.

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Study Tour  

• SAME DEUTZ-FAHR INDIA (P) LTD.

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Website for govt. jobs

http://sarkari-naukri.blogspot.com/2006_09_11_archive.html