stress strain basic-1
TRANSCRIPT
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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
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