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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