Civil Engineering Reference
In-Depth Information
5 (read as
beta
and
gamma
respectively). The beam is undamped,
thus the Rayleigh damping parameters (
fm
and
fk
) are both set to zero. The boundary
condition data indicate one restrained node at the built-in end of the cantilever, where both
freedoms are restrained. There is one loaded freedom (
nlf=1
) in this example at node 2,
sense 1 (the translational freedom). The sinusoidal loading function to be applied has been
input using a total of 12 coordinates comprising 11 coordinates at 0.1 s intervals up to 1
s, followed by a “quiet zone” involving a single interval of 0.8 s up to 1.8 s. The program
linearly interpolates this load/time function at the calculation step length of 0.05 s for the
Newmark algorithm. The final data gives the freedoms at which output is required. In this
example, the displacement, velocity and acceleration under the load are of interest, so there
is just one output required (
nof=1
), again at node 2 sense 1.
The output from Program 11.1 is shown in Figure 11.2 and a plot of the computed
displacement/time history of the cantilever tip is shown in Figure 11.3. For comparison,
β
=
0
.
25 and
γ
=
0
.
There are 2 equations and the skyline storage is 3
Output at node 2, sense 1
time disp velo accel
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.5000E-01 0.1942E-02 0.7768E-01 0.3107E+01
0.1000E+00 0.9511E-02 0.2251E+00 0.2788E+01
0.1500E+00 0.2531E-01 0.4069E+00 0.4485E+01
0.2000E+00 0.5285E-01 0.6946E+00 0.7026E+01
0.2500E+00 0.9488E-01 0.9866E+00 0.4652E+01
0.3000E+00 0.1497E+00 0.1207E+01 0.4159E+01
0.3500E+00 0.2153E+00 0.1415E+01 0.4184E+01
0.4000E+00 0.2892E+00 0.1541E+01 0.8437E+00
0.4500E+00 0.3650E+00 0.1493E+01 -0.2780E+01
0.5000E+00 0.4362E+00 0.1352E+01 -0.2843E+01
0.5500E+00 0.4976E+00 0.1104E+01 -0.7080E+01
0.6000E+00 0.5421E+00 0.6758E+00 -0.1005E+02
0.6500E+00 0.5633E+00 0.1746E+00 -0.9996E+01
0.7000E+00 0.5589E+00 -0.3524E+00 -0.1108E+02
0.7500E+00 0.5261E+00 -0.9574E+00 -0.1312E+02
0.8000E+00 0.4638E+00 -0.1534E+01 -0.9945E+01
0.8500E+00 0.3757E+00 -0.1993E+01 -0.8412E+01
0.9000E+00 0.2659E+00 -0.2397E+01 -0.7734E+01
0.9500E+00 0.1393E+00 -0.2670E+01 -0.3187E+01
0.1000E+01 0.4299E-02 -0.2729E+01 0.8097E+00
0.1050E+01 -0.1284E+00 -0.2581E+01 0.5126E+01
0.1100E+01 -0.2487E+00 -0.2229E+01 0.8928E+01
0.1150E+01 -0.3455E+00 -0.1642E+01 0.1458E+02
0.1200E+01 -0.4081E+00 -0.8625E+00 0.1658E+02
0.1250E+01 -0.4308E+00 -0.4551E-01 0.1610E+02
0.1300E+01 -0.4123E+00 0.7824E+00 0.1701E+02
0.1350E+01 -0.3534E+00 0.1575E+01 0.1468E+02
0.1400E+01 -0.2597E+00 0.2174E+01 0.9284E+01
0.1450E+01 -0.1415E+00 0.2554E+01 0.5935E+01
0.1500E+01 -0.9326E-02 0.2733E+01 0.1196E+01
0.1550E+01 0.1243E+00 0.2614E+01 -0.5935E+01
0.1600E+01 0.2452E+00 0.2221E+01 -0.9787E+01
0.1650E+01 0.3422E+00 0.1660E+01 -0.1265E+02
0.1700E+01 0.4067E+00 0.9181E+00 -0.1702E+02
0.1750E+01 0.4310E+00 0.5512E-01 -0.1750E+02
0.1800E+01 0.4132E+00 -0.7674E+00 -0.1540E+02
Figure 11.2
Results from Program 11.1 example
