Mathcad - krata3t
Mathcad - krata3t
Mathcad - krata3t
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Macierze sztywności elementów kratownicy<br />
Lx e := X Wke<br />
− X Wpe<br />
Ly e := Y Wke<br />
− Y Wpe<br />
L e := Lx e<br />
( )<br />
( )<br />
( )<br />
( )<br />
( ) 2 + ( Ly e ) 2<br />
1<br />
1<br />
1<br />
1<br />
2<br />
3.000<br />
4.000<br />
1<br />
2<br />
2.000<br />
1.000<br />
1<br />
2<br />
3.606<br />
4.123<br />
Lx<br />
3<br />
4<br />
3.000<br />
= m<br />
Ly<br />
5.000<br />
5 5.000<br />
6 2.000<br />
3<br />
4<br />
-3.000<br />
= m<br />
L<br />
0.000<br />
5 0.000<br />
6 -2.000<br />
=<br />
3<br />
4<br />
5<br />
6<br />
4.243<br />
5.000<br />
5.000<br />
2.828<br />
m<br />
J e :=<br />
⎡<br />
( ) 2<br />
E ⋅ A e Lx<br />
⎢ e<br />
( L e ) 3 ⋅<br />
⎢<br />
Lx e ⋅ Ly e<br />
⎣<br />
Lx e ⋅ Ly e<br />
( Ly e ) 2<br />
⎤<br />
⎥<br />
⎥<br />
⎦<br />
7<br />
7.000<br />
7<br />
-2.000<br />
7<br />
7.280<br />
8<br />
2.000<br />
8<br />
3.000<br />
8<br />
3.606<br />
Mimo, że nie jest to potrzebne w dalczych obliczeniach, można pokazać bloki J macierzy sztywności wszystkich elementów<br />
⎛<br />
7658.5 5105.7<br />
9104.7 2276.2 kN<br />
4700.6<br />
J 1 = ⎜<br />
⋅<br />
J 2 = ⎜<br />
⎟ ⋅<br />
J 3 = ⎜<br />
5105.7 3403.8 m<br />
2276.2 569.0 m<br />
−4700.6<br />
⎝<br />
⎞ ⎟⎠<br />
kN<br />
⎛<br />
⎝<br />
⎞<br />
⎠<br />
⎛<br />
⎝<br />
−4700.6<br />
4700.6<br />
⎞<br />
⎟<br />
⎠<br />
⋅<br />
kN<br />
m<br />
⎛<br />
4812.3 0.0<br />
4812.3 0.0 kN<br />
4253.5<br />
J 4 = ⎜<br />
⋅<br />
J 5 = ⎜<br />
⎟ ⋅<br />
J 6 = ⎜<br />
0.0 0.0 m<br />
0.0 0.0 m<br />
−4253.5<br />
⎝<br />
⎞ ⎟⎠<br />
kN<br />
⎛<br />
⎝<br />
⎞<br />
⎠<br />
⎛<br />
⎝<br />
−4253.5<br />
4253.5<br />
⎞<br />
⎟<br />
⎠<br />
⋅<br />
kN<br />
m<br />
⎛<br />
3055.7 −873.0<br />
2053.4<br />
J 7 = ⎜<br />
⋅<br />
J 8 = ⎜<br />
−873.0 249.4 m<br />
3080.1<br />
⎝<br />
⎞ ⎟⎠<br />
kN<br />
⎛<br />
⎝<br />
3080.1<br />
4620.1<br />
⎞<br />
⎟<br />
⎠<br />
⋅<br />
kN<br />
m