16 M3 KobierskiM SzypowskaK ZAD16


" Rama jest dwukrotnie statycznie niewyznaczalna:
" Układ uwolniony (podstawowy):
" Równania kanoniczne dla rozważanej ramy mają postać:
´11X1+ ´12X2+ ´1P=0
´21X1+ ´22X2+ ´2P=0
" Wykresy momentów gnących wywołanych obciążeniem ciągłym:
" Wykresy momentów gnących wywołanych siłą jednostkową X1:
" Wykresy momentów gnących wywołanych siłą jednostkową X2:
" Współczynniki układu równań kanonicznych są następujące:

´11= " " " " + " + " " = + + = "


´12=´21= " " + " " = + =



´22= " " " + + " " " " = + + " " =


= " + " + " = "


´1P= " " " " - " + " - " + " " " - + " " " " =



= - " - " - " + " " = - " " - " " - " " + " " =- " "


-

´2P= " " - " + " " " + " " " + " " " + "2" =


= - " + " " " =


= " " - " = "

" Po podstawieniu współczynników do układu równań kanonicznych otrzymamy:
5 17 " =0/"3"
3" " + " + - "
24
11 1 " 6"
" + " " + " =0/"
3 2

17
5" +3" - " " =0
8
6" +22" "3" " =0
17
" " -3"
8
= =0,425" " -0,6"
5
17
" " -3"
6" 8 +22" +3" " =0
5
2,55" " -3,5" +22" +3" " =0
18,4" =-5,55" "
37
=- " "
120
37
=0,425" " -0,6" - " " =0,61" "
120
" Równania równowagi:

=06" - - + " =0 1

=06" + =0 2


=06" - - " " - "2" =0 3
2

z 1: = " -0,61" " =0,39" "

z 2: =- =- - " " = " "



z 3: = " " "2" - " = " " - " " = " "

" Momenty gnące i siły tnące:
0d" d"
"

= " -
2



= = - "

0d" d"
"

=- + " + "
2

37

= = =- " "
120
0d" d"

= " -

37

=- =- =- " "
120
0d" d"

= " - " -



=- = =0,39" "

I

| =0
"

| =0,61" " - =0,11" "
2

| =0
- " =0

= =0,61"


| , =- " "0,18605+0,3721" " =0,18605" "

| = =0,61" "

| =0,61" " - " =0,39" "
II
"

| =- +0,61" " =0,11" "
2
37 119

| =0,11" " + - " " =- " "
120 600
37

| = | = =- " "
120
III
7

| =- =- " "
60
37 7 23

| = " " - " " = " "
120 60 120
37

| = | =- =- " "
120
IV
37 7 23

| = " " - " " = " "
120 60 120
37 7 119

| = " " -0,39" " - " " =- " "
120 60 600

| = | = =0,39" "
" Siły normalne:
Pręt A-B:
- + =0
37
= =- " "
120
Pręt B-C:
" - - =0
= " -0,61" " =0,39" "
Pręt C-D:
- =0
37
= = " "
120
Pręt D-E:
- =0
= =0,39" "
" Wykresy:
Momentów gnących:
Sił tnących:
Sił normalnych:


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