MAE 156A HW # 0
Problem 1
Given the equations,
x! = x cos 2 + y sin 2 + 2z sin cos
y! = x sin 2 + y cos 2 2z sin cos
z! = z(cos 2 sin 2 ) + ( y x)sin cos
(a) Use trigonometric identities to show that
x+ y x y
+
cos 2 + z sin 2
2
2
y = similar expression i
MAE 156A HW # 2
Problem 1
Problem 1.34 from textbook.
Problem 2
Problem 1.36 from textbook
Problem 3
Problem 1.38 from textbook
Problem 4
Problem 1.41 from textbook. Note: Please use both, formula and Mohrs circle to solve this problem
Problem 5
Problem 1
HW 1 Solution
MAE 156A - Advanced Strength of Materials
October 14, 2014
Problem 1
Given the equations,
x = x cos2 + y sin2 + 2z sin cos
y = x sin2 + y cos2 2z sin cos
z = z(cos2 sin2 ) + (y x) sin cos
(a) Use trigonometric identities to show that
x =
MAE 156A HW # 7 Solution
Problem 1 (Problem 4.14 from textbook)
Problem 2 (Problem 4.38 from textbook)
Problem 3 (Problem 4.40 from textbook)
Problem 4 (Problem 4.42 from textbook)
Problem 5 (Problem 4.43 from textbook)
Problem 6 (Problem 10.7 from textbo
MAE 156A HW #1
Problem 1
A simply supported beam with cross section as shown below is loaded as shown.
Assume that a = 0.2 m, b = 0.1 m and the value of F is not given.
a) Determine location of centroid, area moments and products of inertia of the cross-s
MAE 156A, HW #5
Problem 1:
Problem 5.1 from textbook.
Problem 2:
Problem 5.4 from textbook
Problem 3:
Problem 5.21 from textbook
Problem 4:
Problem 5.22 from textbook
Problem 5:
Problem 5.35 from textbook.
Problem 6:
Problem 5.37 from textbook.
Prof. Ghoniem
1
ADVANCED STRENGTH OF MATERIALS - MAE 156A
Mechanical and Aerospace Engineering Department
University of California, Los Angeles
Midterm, Fall 2014
Time: 110 min
Total points: 100
(5 questions)
an 8/1211 summary sheet is allowed
SOLUTIONS
S
Note: the calculation
below only finds the
magnitude of the
moment; it is acting in
the negative direction,
so use M = -40 Nm
when calculating the
stresses
MAE 156A, HW #4
Problem 1:
Problem 3.2 from textbook.
If the stress field given below acts in the thin plate shown in Fig. P3.1 and p is a known constant,
determine the c s so that edges x = a are free of shearing stress and no normal stress acts on edge
MAE 156A
Midterm
May 2, 2013
Instructor: Ajit Mal
DO ALL WORK ON THIS EXAM
ATTACH ADDITIONAL SHEETS IF NEEDED
USE NOTATIONS AND SYMBOLS INTRODUCED IN CLASS
PLEASE WRITE CLEARLY AND EXPLAIN ALL YOUR STEPS
NAME/UID_
Problem 1_
Problem 2_
Problem 3_
Problem
MAE 156 A
HW # 1
Solution
Problem 1.
Calculate and sketch the shear force, V, and bending moment, M, for the
loaded beam shown. Determine the maximum absolute values of V and M and the
locations where they occur. Assume w = 1 kN/m and L = 2 m.
Solution to
MAE 156A
Advanced Strength of Materials
Instructor: Professor Ajit Mal, 310-825-5481 [email protected]
University of California, Los Angeles
School of Engineering and Applied Science
Mechanical and Aerospace Engineering (MAE) Department
Lecture 1B
Review of e
MAE 156A HW # 4 Solutions
Problem 1:
Problem 2.2 from Textbook
Solution:
Problem 2:
Problem 2.14 from textbook.
Solution:
Problem 3
Problem 2.34 from textbook
Solution:
Problem 4
Problem 2.36 from textbook.
Solution:
Problem 5
Problem 2.38 from textbook.
MAE 156A HW #2
Problem 1
A simply supported beam with cross section as shown below is loaded as shown.
Assume that a = 0.2 m, b = 0.1 m and the value of F is not given.
a) Determine location of centroid, area moments and products of inertia of the cross-s
MAE 156A
Advanced Strength of Materials
Instructor: Professor Ajit Mal, 310-825-5481 [email protected]
University of California, Los Angeles
School of Engineering and Applied Science
Mechanical and Aerospace Engineering (MAE) Department
Lecture 3A
Strain and
MAE 156A
Advanced Strength of Materials
2007 Ajit Mal
Instructor: Professor Ajit Mal, 310-825-5481 [email protected]
University of California, Los Angeles
School of Engineering and Applied Science
Mechanical and Aerospace Engineering (MAE) Department
Text: Ug
HW 0 Solution
MAE 156A - Advanced Strength of Materials
October 14, 2014
Problem 1
Given the equations,
x = x cos2 + y sin2 + 2z sin cos
y = x sin2 + y cos2 2z sin cos
z = z(cos2 sin2 ) + (y x) sin cos
(a) Use trigonometric identities to show that
x =
MAE 156A
Advanced Strength of Materials
2007 Ajit Mal
Instructor: Professor Ajit Mal, 310-825-5481 [email protected]
University of California, Los Angeles
School of Engineering and Applied Science
Mechanical and Aerospace Engineering (MAE) Department
Text: Ug
Buckling Problem
Discussion Week 10
Buckling Problem
Find the member which fails rst and under what type of failure. (Given A = 5.4 105 m2 , I = 3.91
109 m4 , and E = 210GPa)
A
42 MPa
45 deg
C
B
63 MPa
P
L=2.5m
In discussion today, I mixed up two differe
2007 Ajit Mal
Mechanical and Aerospace Engineering Department
MAE 156A, (Advanced) Strength of Materials
Instructor: Professor A. Mal, Ext: 55481, Room 46-147H Engr. IV [email protected]
Prerequisites: MAE 101, MAE 182A or Equivalent
Text: Ugural and Fenster,
MAE 156A HW # 7
Problem 1 (Problem 4.14 from textbook)
Problem 2 (Problem 4.38 from textbook)
Problem 3 (Problem 4.40 from textbook)
Problem 4 (Problem 4.42 from textbook)
Problem 5 (Problem 4.43 from textbook)
Problem 6 (Problem 10.7 from textbook)
Probl
MAE 156A HW #1
Problem 1
A simply supported beam with cross section as shown below is loaded as shown.
Assume that a = 0.2 m, b = 0.1 m and the value of F is not given.
a) Determine location of centroid, area moments and products of inertia of the cross-s
MAE 156A HW # 6
Problem 1 (Problem 6.16 from textbook)
Problem 2 (Problem 6.22 from textbook)
Problem 3 (Problem 8.2 from textbook)
Problem 4 (Problem 8.8 from textbook with z = 0 )
Problem 5 (Problem 8.18 but modified as shown below)
a) Using equations (
MAE 156A HW # 2 Solutions
Problem 1:
Problem 1.34 from textbook
Solution:
Problem 2:
Problem 1.36 from textbook
Solution:
Problem 3:
Problem 1.38 from textbook
Solution:
Problem 4:
Problem 1.41 from textbook. Note: Please use both, formula and Mohrs circl
MAE 156A HW # 3 Solutions
Problem 1:
Problem 2.2 from Textbook
Solution:
Problem 2:
Problem 2.14 from textbook.
Solution:
Problem 3
Problem 2.34 from textbook
Solution:
Problem 4
Problem 2.36 from textbook.
Solution:
Problem 5
Problem 2.38 from textbook.
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