Graphics Programs Reference
In-Depth Information
A uniform beam forms the semiparaboliccantileverarch
AB
. The vertical dis-
placementof
A
due to the force
P
can be shown to be
E I
C
h
Pb
3
δ
A
=
b
where
E I
is the bending rigidity of the beam and
C
h
b
z
2
2
h
b
z
2
1
=
+
1
dz
0
Write aprogram thatcomputes
C
(
h
/
b
)for any givenvalueof
h
/
b
to four decimal
places. Use the program to compute
C
(0
.
5),
C
(1
.
0) and
C
(2
.
0).
=
π/
0
ln(sin
x
)
dx
. A“brute force”method
that works istosplit the integral into several parts: from
x
15.
There is no elegantway to compute
I
=
.
.
0to0
01,from 0
01
to 0
.
2 and from
x
=
0
.
2 to
π/
2. In the first part wecan use the approximation
sin
x
x
, which allows ustoobtain the integral analytically. The other two parts
can beevaluatedwith Gauss-Legendrequadrature. Use this method to evaluate
I
to six decimal places.
≈
16.
h
(m)
620
612
112
80
575
530
425
310
52
35
15
p
(Pa)
0
The pressureofwindwas measuredat variousheights onavertical wall, as shown
on the diagram. Find the height of the pressurecenter, which is definedas
112 m
0
hp
(
h
)
dh
112 m
0
h
=
p
(
h
)
dh
Hint:
fit a cubic polynomial
to
the data and then apply Gauss-Legendre
quadrature.
∗
6.5
Multiple Integrals
Multiple integrals, such as the areaintegral
A
y
)
dx dy
,can also beevaluated
by quadrature. The computations arestraightforward if the region of integration has a
simple geometricshape, such as a triangle oraquadrilateral.Duetocomplications in
f
(
x
,
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