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
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 # 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
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
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
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
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 HW # 3 Solutions
Problem 1:
Problem 1.34 from textbook
Solution:
Problem 2:
Problem 1.36 from textbook
Solution:
1/2
Problem 3:
Problem 1.38 from textbook
Solution:
Problem 4:
Problem 1.41 from textbook. Note: Please use both, formula and Mohrs c
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 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.
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
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
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
Prof. Ghoniem
1
ADVANCED STRENGTH OF MATERIALS - MAE 156A
Mechanical and Aerospace Engineering Department
University of California, Los Angeles
Quiz (1)
For the element shown in the future, considering the x-axis to be along the horizontal face, find:
Th
Mechanical and Aerospace Engineering Department
School of Engineering and Applied Science
MAE 156A, Advanced Strength of Materials
Spring 2017
Homework Assignment 5
Due: May 30th, 2017
1. Solve problem 5.5
2. Solve problem 5.13
3. Solve problem 5.27 (also
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
Mechanical and Aerospace Engineering Department
School of Engineering and Applied Science
MAE 156A, Advanced Strength of Materials
Spring 2017
Homework Assignment 4
Due: May 16, 2017
1. Consider a simply supported beam under uniform load p, as shown in
ta
1
Solving Problem 5.34 using the curved beam formula
For the clamp below, we want to find the maximum force P if the allowable stress all = 80M P a in tension
and compression.
The force P will create maximum tension and compression on the section a-a.
In
Table 6.2. Shear Stress and Angle cf Twist uflarinus hlembcm in Torsion
Maximum Angle of mist
Crass xecricn shaming mm per cm": length
=cfw_a2 + .52)?"
=:; EEG
Fcr circular bar: a: b
Equilatcral triangle
(J III- I-J'IJ'J'JI"
34'-
t 15:;
lu-m 'l'l'