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Machine Component Design

(INME 4011)- Prof. Pablo G. Caceres-Valencia

1st Exam

Student Number :___________________ Name: _________________________________

Section (circle): 7:30AM 9:00AM Date: October 12th

, 2015

Notes: This is an open book examination. Others items needed are calculators, pencils, pens andrulers. Please ensure that you have a complete copy of the exam. Only clear and concise answerswill be considered. Total Points = 100. Time Allowed: 120 minutes

-------------------------------------------------------------------------------------------------------1. (70 points) The component below has been made of a steel pipewith an outside diameter

(OD) of 170mmand a thickness (t) of 6mm. A design safety factor of 3was used in thiscomponent. The internal pressure in the pipe is 5000kPaand there are twoconcentrated loads

acting at the end B, one in the positive x-direction (F=6000N) and the other in the negativey-direction (P=7000N). Determine if the component has been properly designed if the materialhas a yield stress of 520MPa.

Data: a=600mm , b=900mm , c=600mm ,Elastic Modulus = 200GPa;Poissons ratio = 0.3.

Stress Concentration factors at the wall : Kbending=1.7 , Ktorsion=1.6 , Kshear=1.4 , Kaxial-pressure=1.8.If a delta strain rosette is placed in the point H (K), with one of the strain gauges (a) parallel to

the x-direction and the triangle pointing towards the positive z-direction (y-direction), what willbe the readings in the strain gauges a, b and c (see figure below).

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You should do the calculation for the point .............. H KTo receive full points, you must draw the direction of the stresses on the cube elements

Write the formula and the results in the given area

Area (A)

Moment of

Inertia (I) and

(J)

G- modulus

Stresses due to

force in x-

direction (F)

Stresses due to

force in y-

direction (P)

y

z

x

y

z

x

y

z

x

y

z

x

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Stresses due to

pressure

Total Normal

Stresses(indicate

subscript)

Total Shear

Stresses

(indicatesubscripts)

Stress Tensor

PrincipalStresses

Angles for the

principal

stresses

DET Theory

Von Mises

Stress and

Safety factor

y

z

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

x

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MSS Theory,

Maximum

Shear Stress

and Safety

Factor

Draw Mohr

Circle for

stresses

Was thecomponent

properly

designed

Compliance

Matrix

Calculated

Strains

Strain Tensor

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Principal

strains

Angles for the

principal strain

Mohr!s Circle

for strains

Strain in the

strain gauges a,

b and c ( for

the point K

change the y-

direction for a

z-direction in

the figure)

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2. (30 points) The figure below shows a 60oangle (angle between the x-axis and the direction 1

of the fibers) graphite/epoxy lamina which is subjected to the following stresses: !x = 2MPa ,

!y = -3MPa and "xy = 4MPa. What will be the strains associated with a delta rosette strain gaugeattached to the surface of the lamina? Data: E1=181GPa , E2=10.3GPa , #12=0.28 , #23=0.6 ,

#13=0.27 , G12=7.17GPa , G23=3.0GPa , G31=7.00GPa

#21

transformationmatrix

Stresses at 1-2coordinate

system

Reduced

Compliance

matrix

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$1

$2

%12

Transformation

Matrix

$x$y

%xy

$a$b

$c

Principal Stresses

Angle for

Principal Stresses

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Principal Strains

Angle for

Principal Strains