C.2plotting 79
- 2D plotting
A simply supported beam that is subjected to a constant distributed load
wover two-thirds of its length is shown in Figure 21. The deflectiony,
x
y
w
2L/3 L/3
Figure 21: A simply supported beam
as a function ofx, is given by the equations:
y=24LEI−wx
(
Lx^3 −^169 L^2 x^2 +^6481 L^4
)
for 06 x 623 L,
y=−wL
54EI
(
2x^3 −6Lx^2 +^40
9
L^2 x−^4
9
L^3
)
for^2
3
L 6 x 6 L,
whereEis the elastic modulus,Iis the moment of inertia, andLis
the length of the beam. For the beam shown in Figure 21,L=20 m,
E= 200 × 109 Pa(steel),I= 348 × 10 −^6 m^4 , andw= 5 × 103 N/m.
Make a plot of the deflection of the beamyas a function ofx.
- 3D plotting
An anti-symmetric cross-ply composite laminate has two layers where
fibres are aligned perpendicular to one another. A laminate of this type
will deform into a saddle shape due to residual thermal stresses as
described by the equation:
w=k(x^2 −y^2 ),
wherexandyare the in-plane coordinates,wis the out-of-plane deflection„
andkis the curvature (a complicated function of material properties
and geometry). Make a 3dsurface plot showing the deflection of a 100
× 100 mm square plate (− 50 6 x 6 50 ,− 50 6 y 650 ) assuming
k=0.254 mm−^1.
