Advanced Methods of Structural Analysis

Appendix 583

Ta b l e A. 2 4 Special functions for stability analysis
Functions Form 1 Form 2 Maclaurin series

' 1 . /
^2 tan
3.tan/

1

3

^2 sin

sincos

1 

2

15



4

525

C

' 2 . /
.tan/
8 tan



tan

2



2



1

4

sin^2 cos

2  2 cossin

1 

2

30

11

4

25200

C

' 3 . /
.sin/
4 sin



tan

2 



2



1

2

.sin/

2  2 cossin

1 C

2

60 C

13^4

25200 C

' 4 . / ' 1



2

 1

6

^2 sin

2 sincos

1 

2

60

 

4

84000

C

1 . /
^3
3.tan/

1

3

^3 cos

sincos

1 2

2

5



4

525

C

2 . / (^1)

2
 1
12
^3 .1Ccos/
2 sincos
1 
^2
10

^4
8400
C

sin

sin

sin
1 C
^2
6
C
7^4
360
C

tan

tan
cos
sin
1 
^2
3

^4
45
C
tan tan
sin
cos
0 C^2 C
^4
3
C
Numerical values of these functions in terms of dimensionless parameterare presented in
Ta b l eA.25
Ta b l e A. 2 5 Special functions for stability analysis by Displacement method
' 1 . / ' 2 . / ' 3 . / ' 4 . /
1 . /
2 . /
0.0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.2 0.9973 0.9980 1.0009 0.9992 0.9840 0.9959
0.4 0.9895 0.9945 1.0026 0.9973 0.9362 0.9840
0.6 0.9756 0.9881 1.0061 0.9941 0.8557 0.9641
0.8 0.9566 0.9787 1.0111 0.9895 0.7432 0.9362
1.0 0.9313 0.9662 1.0172 0.9832 0.5980 0.8999
1.1 0.9164 0.9590 1.0209 0.9798 0.5131 0.8789
1.2 0.8998 0.9511 1.0251 0.9757 0.4198 0.8557
1.3 0.8814 0.9424 1.0298 0.9715 0.3181 0.8307
1.4 0.8613 0.9329 1.0348 0.9669 0.2080 0.8035
1.5 0.8393 0.9226 1.0403 0.9619 0.0893 0.7743
 =2 0.8225 0.9149 1.0445 0.9620 0.0000 0.7525
1.6 0.8153 0.9116 1.0463 0.9566 0:0380 0.7432
1.7 0.7891 0.8998 1.0529 0.9509 0:1742 0.7100
1.8 0.7609 0.8871 1.0600 0.9448 0:3191 0.6747
1.9 0.7297 0.8735 1.0676 0.9382 0:4736 0.6374
2.0 0.6961 0.8590 1.0760 0.9313 0:6372 0.5980
2.1 0.6597 0.8437 1.0850 0.9240 0:8103 0.5565
2.2 0.6202 0.8273 1.0946 0.9164 0:9931 0.5131
(continued)