Ae/ME/CE/AM 102c Spring 2013 Mechanics of Solids and Structures - Homework 3 Due April 25, 9:00AM, in class.

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Ae/ME/CE/AM 102c Spring 2013
Mechanics of Solids and Structures - Homework 3
Due April 25,9:00AM,in class.
Instructor;G.Ravichandran,205-Firestone,ravi@caltech:edu,x4525
Oce Hours:
 Bharat Penmecha,bharat@caltech:edu,SFL-Group Study 2-3,Mondays 5-6.00 PM
 Pinaky Bhattacarya,pinaky
b@caltech:edu,TOM 014,Wednesdays,5.30-6.30 PM
Problem 1
Consider a Single-Edged Notched Panel under tension (SENT) made of an aircraft aluminium alloy Al
2024-T351.For SENT,the stress intensity factor (SIF) is of the form
K
I
= 
1
p
aF

a
W

(1)
where shape factor,F(a=W) is of the form
F(a=W) =
h
1:12 0:23

a
W

+10:55

a
W

2
21:71

a
W

3
+30:38

a
W

4
i
(2)
The nominal critical stress intensity factor for the material is K
Ic
= 30MPa
p
m.The yield stress is 324
MPa and the ultimate tensile strength is 469 MPa.Young's modulus and Poisson's ratio are,73 GPa
and 0.33 respectively.
Figure 1:Problem 1
1.If the panel width (W) is 60mm and the crack length,a,is 20mm,estimate the critical stress at
the crack initiation.What is the critical stress (
c
) as fraction of the ultimate stress.
2.If the design stress is 20% of the ultimate stress,estimate the critical crack length (a
c
) the panel
can tolerate?
Problem 2
Consider a center crack of length (2a) in a large plate made up of linearly elastic material subject to
anti-plane shear loading (mode III) with a far eld stress 
1
.
 Derive the stress and displacement elds,u
3
= w(x
1
;x
2
).Formulate the governing equation in
terms of w and use the traction free boundary conditions in terms of displacement.
1
 Using these elds derive the asymptotic stress and displacement elds around the crack tip and
the Stress Intensity factor K
III
.(Use the approximation r=a << 1)
Problem 3
Consider a crack of length 2a that makes an angle  with the y-axis in an innite plane subject to far
eld stresses  and  along the y and x directions as shown.Derive the expressions for the singular
stress components.
Figure 2:Problem 3
2