60 kN 4 m 15 kN/m E 210 GPa I 104 m A 102 m2 5 kN 6 m 8 m Fig.1 e*s
Homework Answers
E=210*10^6;
I=1*10^-4;
A=1*10^-2;
k 1=
10^5 *
[3.5000 0 0 -3.5000 0 0
0 0.0117 0.0350 0 -0.0117 0.0350
0 0.0350 0.1400 0 -0.0350 0.0700
-3.5000 0 0 3.5000 0 0
0 -0.0117 -0.0350 0 0.0117 -0.0350
0 0.0350 0.0700 0 -0.0350 0.1400]
T 1=
0 1 0 0 0 0
-1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
0 0 0 -1 0 0
0 0 0 0 0 1
Kele1 =
10^5 *
0.0117 0 -0.0350 -0.0117 0 -0.0350
0 3.5000 0 0 -3.5000 0
-0.0350 0 0.1400 0.0350 0 0.0700
-0.0117 0 0.0350 0.0117 0 0.0350
0 -3.5000 0 0 3.5000 0
-0.0350 0 0.0700 0.0350 0 0.1400
k2(local) =
10^5 *
3.7123 0 0 -3.7123 0 0
0 0.0139 0.0394 0 -0.0139 0.0394
0 0.0394 0.1485 0 -0.0394 0.0742
-3.7123 0 0 3.7123 0 0
0 -0.0139 -0.0394 0 0.0139 -0.0394
0 0.0394 0.0742 0 -0.0394 0.1485
T 2=
0.7071 0.7071 0 0 0 0
-0.7071 0.7071 0 0 0 0
0 0 1.0000 0 0 0
0 0 0 0.7071 0.7071 0
0 0 0 -0.7071 0.7071 0
0 0 0 0 0 1.0000
Kele(2) =
10^5 *
1.8631 1.8492 -0.0278 -1.8631 -1.8492 -0.0278
1.8492 1.8631 0.0278 -1.8492 -1.8631 0.0278
-0.0278 0.0278 0.1485 0.0278 -0.0278 0.0742
-1.8631 -1.8492 0.0278 1.8631 1.8492 0.0278
-1.8492 -1.8631 -0.0278 1.8492 1.8631 -0.0278
-0.0278 0.0278 0.0742 0.0278 -0.0278 0.1485
k 3=
10^5 *
3.7123 0 0 -3.7123 0 0
0 0.0139 0.0394 0 -0.0139 0.0394
0 0.0394 0.1485 0 -0.0394 0.0742
-3.7123 0 0 3.7123 0 0
0 -0.0139 -0.0394 0 0.0139 -0.0394
0 0.0394 0.0742 0 -0.0394 0.1485
T3 =
0.7071 -0.7071 0 0 0 0
0.7071 0.7071 0 0 0 0
0 0 1.0000 0 0 0
0 0 0 0.7071 -0.7071 0
0 0 0 0.7071 0.7071 0
0 0 0 0 0 1.0000
Kele(3) =
10^5 *
1.8631 -1.8492 0.0278 -1.8631 1.8492 0.0278
-1.8492 1.8631 0.0278 1.8492 -1.8631 0.0278
0.0278 0.0278 0.1485 -0.0278 -0.0278 0.0742
-1.8631 1.8492 -0.0278 1.8631 -1.8492 -0.0278
1.8492 -1.8631 -0.0278 -1.8492 1.8631 -0.0278
0.0278 0.0278 0.0742 -0.0278 -0.0278 0.1485
k 4=
10^5 *
3.5000 0 0 -3.5000 0 0
0 0.0117 0.0350 0 -0.0117 0.0350
0 0.0350 0.1400 0 -0.0350 0.0700
-3.5000 0 0 3.5000 0 0
0 -0.0117 -0.0350 0 0.0117 -0.0350
0 0.0350 0.0700 0 -0.0350 0.1400
T 4=
0 1 0 0 0 0
-1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
0 0 0 -1 0 0
0 0 0 0 0 1
Kele(4) =
10^5*
0.0117 0 -0.0350 -0.0117 0 -0.0350
0 3.5000 0 0 -3.5000 0
-0.0350 0 0.1400 0.0350 0 0.0700
-0.0117 0 0.0350 0.0117 0 0.0350
0 -3.5000 0 0 3.5000 0
-0.0350 0 0.0700 0.0350 0 0.1400
Kglobal=10^5 *
0.0117 0 -0.0350 -0.0117 0 -0.0350 0 0 0 0 0 0 0 0 0
0 3.5000 0 0 -3.5000 0 0 0 0 0 0 0 0 0 0
-0.0350 0 0.1400 0.0350 0 0.0700 0 0 0 0 0 0 0 0 0
-0.0117 0 0.0350 1.8748 1.8492 0.0072 -1.8631 -1.8492 -0.0278 0 0 0 0 0 0
0 -3.5000 0 1.8492 5.3631 0.0278 -1.8492 -1.8631 0.0278 0 0 0 0 0 0
-0.0350 0 0.0700 0.0072 0.0278 0.2885 0.0278 -0.0278 0.0742 0 0 0 0 0 0
0 0 0 -1.8631 -1.8492 0.0278 3.7262 0 0.0557 -1.8631 1.8492 0.0278 0 0 0
0 0 0 -1.8492 -1.8631 -0.0278 0 3.7262 0 1.8492 -1.8631 0.0278 0 0 0
0 0 0 -0.0278 0.0278 0.0742 0.0557 0 0.2970 -0.0278 -0.0278 0.0742 0 0 0
0 0 0 0 0 0 -1.8631 1.8492 -0.0278 1.8748 -1.8492 0.0072 -0.0117 0 0.0350
0 0 0 0 0 0 1.8492 -1.8631 -0.0278 -1.8492 5.3631 -0.0278 0 -3.5000 0
0 0 0 0 0 0 0.0278 0.0278 0.0742 0.0072 -0.0278 0.2885 -0.0350 0 0.0700
0 0 0 0 0 0 0 0 0 -0.0117 0 -0.0350 0.0117 0 -0.0350
0 0 0 0 0 0 0 0 0 0 -3.5000 0 0 3.5000 0
0 0 0 0 0 0 0 0 0 0.0350 0 0.0700 -0.0350 0 0.1400
F+Ff=Kglobal*d
F=Nodal forces
Ff=lump vector
d=nodal displacement
d=
0
0
0
-0.0608
-0.0002
0.0078
-0.0530
-0.0083
-0.0075
-0.0449
-0.0001
0.0117
0
0
0
F =
43.6514
72.0911
-158.1780
5.0000
0.0000
0.0000
0.0000
-60.0000
0.0000
-0.0000
0.0000
0.0000
11.3486
47.9089
-75.0930
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