For the given Mohr's circle where o, = 40 MPa,try = 40 MPa, (i) what is the maximum shear stress tmax, (ii) what are the maximum and minimum normal stresses omax and omin, and (iii) what is the angle of the principal plane 0,? -50 (40, 40) (0, 0) (40, 0) (80, 0) 50 100 |(40, –40) -50

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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Problem 1.1MA
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Answer the problem with detailed step by step solution refer to the table of equations when answering the problem.
TABLE OF EQUATIONS
Normal Stress
Bearing Stress
P
A
td
Shear Stress (Single)
Shear Stress (Double)
P
= 1
2A
Tangential Stress (Cylindrical)
PD Pr
O = =T
Longitudinal Stress (Cylindrical)
PD Pr
O = 2t
4t
Stress on Spherical Vessels
Hooke's Law
PD Pr
Os =
4t
O = Ee
2t
Deformation
Axial Strain
PL
ΔΙ.
E =
AE
1-1-,
Generalized Hooke's Law
dy
E
Ex =
Dilatation
dy
Ey =
E
e = €x + €y + €z
E
dy
E, = -v
E
E
Shear Strain
Shear Modulus
E
G =
2(1+ v)
y =
Thermal Strain
Thermal Deformation
8, = a(AT)L
ET = aAT
Shear Stress due to Torsion
Shear Stress at any Point
Tc
Tmax =
T=-Tmax
Polar Moment of Inertia of Circle
Minimum Shear Stress (Hollow)
Tmin =-Tmax
C2
Angle of Twist
Polar Moment of Inertia of Hollow Circle
TL
JG
Shear Stress due to Torsion (Non-Circular Tubes)
Power
T
P = T
2tA
Angle of Twist (Non-Circular Tubes)
TL ( ds
Bending Stress
Ox = --om
4A?G
Maximum Bending Stress
Mc
Om =T
Elastic Section Modulus
Deflection of a Beam
d?y
Edr = M
Second Moment-Area Theorem
tc/p = (area bet.C and D)x
Area of General Spandrel
bh
A =
n+1
Centroid of General Spandrel
b
n+2
Deflection in Simply Supported Beams
8p = 0Ạx - tạ/A
tc/A
Deflection in Cantilever Beams
8R = (area of M/El diagram)Xg
Maximum and Minimum Stress in Beams with
Combined Axial and Lateral Loads in Beams
Combined Axial and Lateral Loads
P My
A I
P. Mc
Omax,min = t-
O =--
Transformation of Plane Stress
cos 20 +Txy sin 20
2
Principal Stresses
O + dy Ox - 0y
2
Ox-dy sin 20 + Tyy cos 20
2
cos 20 - Tzy sin 20
Omar, min=
2
Maximum Shear Stress and Corresponding Angle
Angle of Principal Plane
+ Tây
Tmax =
21.xy_
O- dy
2Txy
tan 20
tan 20,
%3D
Coordinates of Center of Mohr's Circle
(*.0)
(0x+ dy
2
Transcribed Image Text:TABLE OF EQUATIONS Normal Stress Bearing Stress P A td Shear Stress (Single) Shear Stress (Double) P = 1 2A Tangential Stress (Cylindrical) PD Pr O = =T Longitudinal Stress (Cylindrical) PD Pr O = 2t 4t Stress on Spherical Vessels Hooke's Law PD Pr Os = 4t O = Ee 2t Deformation Axial Strain PL ΔΙ. E = AE 1-1-, Generalized Hooke's Law dy E Ex = Dilatation dy Ey = E e = €x + €y + €z E dy E, = -v E E Shear Strain Shear Modulus E G = 2(1+ v) y = Thermal Strain Thermal Deformation 8, = a(AT)L ET = aAT Shear Stress due to Torsion Shear Stress at any Point Tc Tmax = T=-Tmax Polar Moment of Inertia of Circle Minimum Shear Stress (Hollow) Tmin =-Tmax C2 Angle of Twist Polar Moment of Inertia of Hollow Circle TL JG Shear Stress due to Torsion (Non-Circular Tubes) Power T P = T 2tA Angle of Twist (Non-Circular Tubes) TL ( ds Bending Stress Ox = --om 4A?G Maximum Bending Stress Mc Om =T Elastic Section Modulus Deflection of a Beam d?y Edr = M Second Moment-Area Theorem tc/p = (area bet.C and D)x Area of General Spandrel bh A = n+1 Centroid of General Spandrel b n+2 Deflection in Simply Supported Beams 8p = 0Ạx - tạ/A tc/A Deflection in Cantilever Beams 8R = (area of M/El diagram)Xg Maximum and Minimum Stress in Beams with Combined Axial and Lateral Loads in Beams Combined Axial and Lateral Loads P My A I P. Mc Omax,min = t- O =-- Transformation of Plane Stress cos 20 +Txy sin 20 2 Principal Stresses O + dy Ox - 0y 2 Ox-dy sin 20 + Tyy cos 20 2 cos 20 - Tzy sin 20 Omar, min= 2 Maximum Shear Stress and Corresponding Angle Angle of Principal Plane + Tây Tmax = 21.xy_ O- dy 2Txy tan 20 tan 20, %3D Coordinates of Center of Mohr's Circle (*.0) (0x+ dy 2
For the given Mohr's circle where ơx = 40 MPa,try = 40 MPa, (i) what is the
maximum shear stress tmax, (ii) what are the maximum and minimum normal
stresses ơmax and omin, and (iii) what is the angle of the principal plane 0,?
-50
(40, 40)
(0, 0)
(40, 0)
(80, 0)
50
100
|(40, –40)
-50-
Transcribed Image Text:For the given Mohr's circle where ơx = 40 MPa,try = 40 MPa, (i) what is the maximum shear stress tmax, (ii) what are the maximum and minimum normal stresses ơmax and omin, and (iii) what is the angle of the principal plane 0,? -50 (40, 40) (0, 0) (40, 0) (80, 0) 50 100 |(40, –40) -50-
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