UNIVERSITY OF CALIFORNIA, BERKELEY
College of Engineering
Mechanics of Structures (CE130N)
HOMEWORK VII (due on next Friday, March 16th)
Problem 1.(20pts)
Consider a doubly built-in beam of length L with a transverse load of magnitude P in the positive
di
SID 20927483
Due 2/17/12
CE130N
Andreanna 'lzortzis HO /
10
Homework 4
1. The code was changed as follows to give us the compatibility matrix A and the
diagonal matrix. However. we can also nd this by hand to verify that the code is
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UNIVERSITY OF CALIFORNM, BERKELEY
-of-
Mechanics o Materials (eE130)Section I
f
The Second Mid-term Examination
Problem 1 (25points)
.
Draw &mu & moment diagrams for the fobwing h a m (see:Fig. 1 ) and l b the pcalr valucs
a1
for the m r q a n d i n g d u
3.24
(a) Let X be the number of trucks arriving in a 5-minute period.
Given: truck arrival has mean rate = 1 (truck) / minute; hence with
t = 5 minutes = t = 5 (trucks)
Hence P(X 2) = 1 - P(X < 2)
= 1 - P(X = 0) - P(X = 1)
= 1 - e-5 - 5e-5
0.96
(b) Given
3.23
Given: = mean flaw rate = 1 (flaw) / 50m2;
t = area of a panel = 3m x 5m = 15m2
Let X be the number of flaws found on area t. X is Poisson distributed, i.e.
f(x) = e
x
x!
with
= t = 15 / 50 = 0.3 (flaws)
(a)
P(replacement) = 1 - P(0 or 1 flaw)
= 1 -
3.22 The return period (in years) is defined by =
1 where p is the probability of flooding per year. p
Therefore, the design periods of A and B being A = 5 and B = 10 years mean that the respective yearly flood probabilities are P(A) = 1/ (5 years) = 0.2
3.21
(a)
Let X be the number of accidents in two months. X has a Poisson distribution with
3
2 months = 0.5, hence
X =
12 months
0.5
P(X = 1) = e
0.5 0.303, whereas
(3/12)(4)
2
[(3/12)(4)] / 2!
P(2 accidents in 4 months) = e
1
= e /2! 0.184
No, P(1 accid
3.20
(a)
Let X be the number of accidents along the 20 miles on a given blizzard day. X has a
1
20 miles = 0.4, hence
Poisson distribution with X =
50 miles
0.4
P(X 1) = 1 P(X = 0) = 1 e
= 1 0 670320046 0.33
(b)
Let Y be the number of accident-free days a