Curs 13 Aplicatii
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Transcript of Curs 13 Aplicatii
7/17/2019 Curs 13 Aplicatii
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CURS 13
APLICAŢII
1. GRINZI DREPTE
2. GRINZI COTITE
3. CADRE TRIPLU ARTICULATE
4. GRINZI CU ZABRELE (rezolvae !r"# $eo%a &e'"#"lor)
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2 m 2 m 2 m 2 m 2 m
5 t10 t 5 t 5 t
VA+ VB = 25 t
5 x 2 + 10 x 4 + 5 x 6 + 5 x 10 = VB x 8
VB = 16,25 t;
VA= 25 t – 16,25 t = 8,75 t
VA= 8,75 t VB = 16,25 t
8,75 t5 t
3,75 t
11,25 t
6,25 t
5 t
10 t
5 t
16,25 t
5 t
T
++
*
1. GRINZI DREPTE
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2 m 2 m 2 m 2 m 2 m
5 t 10 t 5 t 5 t
MD = 8,75 t x 2 m = 17,5 tm
ME = 8,75 t x 4 m - 5 t x 2 m = 25 tm
ME = 8,75 t x 6 m - 5 t x 4 m – 10 t x 2 m
= 12,5 tm
MB= 8,75 t x 8 m - 5 t x 6 m – 10 t x 4 m
– 5 t x 2 m = - 10 tm
VA= 8,75 t VB = 16,25 t
A
+
B
E CFD
17,5 tm
25 tm
12,5 tm
10 tm
+
*
1. GRINZI DREPTE
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8 m 2 m
5 t/m5 t
VA= 18,75 tVB = 26,25 t
A
T
BC
18,75 t
21,25 t
5 t10 t
+
*
VA+ VB = 5 t/m x 8 m + 5 t = 45 t
5 x 8 x 4 + 5 x 10 = VB x 8
VB = 26,25 t;
VA= 45 t – 26,25 t = 18,75 t
TB = 18,75 t – 5 x 8 t = - 21,25 t
x / 8- x = 18,75/21,25
21,25 x = 18,75 (8 – x)x (21,25 + 18,75) = 150
x = 150/40 = 3,75 m
+
26,25 tx = 3,75 m
1. GRINZI DREPTE
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8 m 2 m
5 t/m5 t
VA= 18,75 t VB = 26,25 t
A
+
BC
35,156 tm
10 tm
+
*
MMA = 18,75 t x 3,75 m – 5 x 3,75 x 3,75/2 t m
= 35,156 tm
MB !"#$%t$ = - (5 t x 2 m) = - 10 tm
x = 3,75
m
1. GRINZI DREPTE
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VA+ VB = 10 t
&A= 2 t/m x 5 m = 10 tMA= 0 = 2 t/m x 5 m + 10 t x 2 m – 4 x VB
VB = 7,5 t
VA= 10 t - VB = 2,5 t
VA= 2,5 t 4 m
5 m
2 t/m10 t
&A= 10 t
VB = 7,5 t2 m
2. GRINZI COTITE
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VA= 2,5 t 4 m
5 m
2 t/m10 t
&A= 10 t
VB = 7,5 t
2 m T
+
&A= 10 t
VA= 2,5 t 10 t
VB = 7,5 t
MC= 10 t x 5 m – 2 t/m x 5 mx 5/2 m = 25 tm
MD= - ( - 7,5t x 2 m) = 15 tm
MC= 25 tm
MD= 15 tm+
+
+
-
D
C
2. GRINZI COTITE
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VA= 2,5 t 4 m
5 m
2 t/m10 t
&A= 10 t
VB = 7,5 t
2 m N
VA= 2,5 t
*
'00
D
C
2. GRINZI COTITE
+
MC= 25 tm
MD= 15 tm
+
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VA= 5 t 4 m
5 m
1 t/m5 t
&A= 5 t
2 mC
B
VA= 5 t
&A= 1 t/m x 5 m = 5 t
MA= 1 t/m x 5 mx 2,5 m + 5 t x 2 m =22,5 tm
MA= 22,5 tm
2. GRINZI COTITE
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VA= 5 t
5 m
1 t/m5 t
&A= 5 t
2 mC
B
MA= 22,5 tm
2. GRINZI COTITE
C
B
5 t
* N
C
5 t
+
T
B+
A= VA= 5 t
B = - 5 t +1 t/m x 5 m=0
TA= &A = 5 t
TB$% *t%= 5 t - 1 t/m x 5 m = 0
TB$% ".!$
= 5 t
T= 5 t - 5 t = 0
5 t
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VA= 5 t
5 m
1 t/m5 t
&A= 5 t
2 mC
B
MA= 22,5 tm
2. GRINZI COTITE
CB
22,5 tm
*+
C
,
B
MA= - 22,5 tm
MB$% *t% = - 22,5 tm +1 t/m x 5 m x 2,5 m = -10tm
MB$% ".!$ = -( 5t x 2m) = - 10 tm
10 tm *'00
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5 m 5 m
6 m
5t/m
2t/m
5 m 5 m
6 m
5t/m
3. CADRE TRIPLUARTICULATE
VA
&B
VB
&A
C
BA
ED
VA + VB = 5 t/m x 10 m = 50 t 2 t/m x 6 m – &A – &B = 0
&A + &B = 2 t/m x 6 m = 12 t
MA= 2t/m x 6 m x 3 m + 5 t/m x 10 m x 5 m
– VB x 10 m = 0VB x 10 m = 36 tm + 225 tm = 261 tm
VB = 26,1 t
VA= 50 t - 26,1 t = 23,' t VA= 23,' t
M,*t.$ = VA x 5 m + &A x 6 m – 2 t/m x 6 m x 3 m
– 5 t/m x 5 m x 2,5 m = 0
&A x 6 m = 36 t m + 62,5 tm – 23,8 t x 5 m = - 1' tm
&A = - 3,167 t
&B = 12 t – (- 3,167 t) = 15,167 t
2t/m
7/17/2019 Curs 13 Aplicatii
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5 m 5 mVA= 23,' t VB = 26,1 t
&A = 3,167 t
C
BA
ED
6 m
5t/m
2t/m
&B = 15,167 t
23,' t
A= 23,' t
D =3,167 t + 2 t/m x 6 m = 15,167 t
E =23,' t – 5 t/m x 10 m = - 26,1 t
26,1 t
15,167 t
* *
*
N
3. CADRE TRIPLUARTICULATE
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5 m 5 mVA= 23,' t VB = 26,1 t
&A = 3,167 t
C
BA
ED
6 m
5t/m
2t/m
&B = 15,167 t
3,167 t
TA= 3,167 t
TD$% *t% = 3,167 t + 2 t/m x 6 m = 15,167 t; TD$% ".!$ = 23,' t
TE $% ".!$= 23,' t – 5 t/m x 10 m = - 26,1 t
TE $% *t%= 3,167 t + 2 t/m x 6 m = 15,167 t
TC = 23,' t – 5t/m x 5 m = - 1,1 t
26,1 t
15,167 t
*
*
+
T
23,' t 15,167 t1,1 t
+
3. CADRE TRIPLUARTICULATE
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3,167 t
26,1 t
15,167 t
*
*
+
T
23,' t 1,1 t
+
15,167 t 23,' t
1,1 t
26,1 t
5 m5 m
x
x / 5-x = 1,1 / 23,'
23,' x = 5,5 – 1,1 x
25 x = 5,5
x = 5,5 / 25 = 0,22 m
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5 m 5 mVA= 23,' t VB = 26,1 t
&A = 3,167 t
C
BA
ED
6 m
5t/m
2t/m
&B = 15,167 t
MA= 0
MD$% *t% = - 3,167 t x 6 m - 2 t/m x 6 m x 3 m = - 55,002 tm;
MD$% ".!$ = - 55,002 tm
M = 0; ME $% *t%= - ( 15,167 t x 6 m ) = - '1,002 tm
Mm$x = 23,' t x 4,78 m – 3,167 t x 6 m – 2 t/m x 6 m x 3 m – 5 t/m x 4,78 m x 4,78m/2 =114,242 tm – 1',002 + 36 + 57,121 tm = 2,11' tm
55,002 tm
*
*
-
+
'1,002 tm
+
3. CADRE TRIPLUARTICULATE
-
x = 0,22 m4,78 m
Mm$x = 2,11' tm
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10 t 10 t 10 t 10 t 10 t5 t 5 t
3 m 3 m 3 m 3 m 3 m3 m
3 m
18 m
4. GRINZI CU Z-BRELEDETER+INAREA EORTURILOR DIN BARE
UTILIZÎND METODA SECŢIUNILOR
AB
VA= 30 t VB = 30 t
10 t 10 t 10 t 10 t 10 t5 t 5 t
3 m 3 m 3 m 3 m 3 m3 m
3 m
18 m
AB
VA= 30 t
CD
$ !
= 0 VA + VB = 5 x 10 t + 2 x 5 t = 60 t
VA = VB = 30 t
= 0 - C + + D x * 450= 0
M = 30 t x ' m – 5 t x ' m – 10 t x 6 m – 10 t x 3 m
– C x 3 m = 0
C = 30 x 3 – 5 x 3 – 10 x 2 – 10 = 45 t; C = 45 t
M$ = 30 t x 6 m – 5 t x 6 m – 10 t x 3 m – x 3 m = 0
= 30 x 2 – 5 x 2 – 10 = 40 t; = 40 t
D x * 450= C - = 5 t; D = 5 2 t
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10 t 10 t 10 t 10 t 10 t5 t 5 t
3 m 3 m 3 m 3 m 3 m3 m
3 m
AB
10 t 10 t 10 t 10 t 10 t
5 t5 t
VA= 30 t VB = 30 t
25 t
25 t
15 t
15 t
5 t5 t
=450
TD
T = D * α
D = 5 t / * 45 0= 5 2 t
T
4. GRINZI CU Z-BRELEDETERMINAREA EFORTURILOR DIN
DIAGONALE
D = T/cos α
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10 t 10 t 10 t 10 t 10 t5 t 5 t
3 m 3 m 3 m 3 m 3 m3 m
AB
10 t 10 t 10 t 10 t 10 t
5 t5 t
VA= 30 t VB = 30 t$ 1
M1 = 25 t x 3 m = 75 tmM$ = 25 t x 6 m – 10 t x 3 m = 120 tm
M = 25 t x ' m – 10 t x 6 m – 10 t x 3 m= 135 tm
M1 = 75 tm
M$ = 120 tm
M = 135 tm
C
D
$
M$
M$ = x
3 m
M$ = 120 tm = x 3 m
= 40 t
I = Ma/h
4. GRINZI CU Z-BRELEDETERMINAREA EFORTURILOR DIN TALPA
INFERIOARA
+
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10 t 10 t 10 t 10 t 10 t5 t 5 t
3 m 3 m 3 m 3 m 3 m3 m
AB
10 t 10 t 10 t 10 t 10 t
5 t5 t
VA= 30 t VB = 30 t$ 1
M = 25 t x ' m – 10 t x 6 m – 10 t x 3 m= 135 tm
M1 = 75 tm
M$ = 120 tm
M = 135 tm
C
D
$
MC
MC = C x
3 m
M = 135 tm = C x 3 m
C = 45 t
C = Mc/h
4. GRINZI CU Z-BRELEDETERMINAREA EFORTURILOR DIN TALPA
SUPERIOARA
+
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4 m 4 m 4 m4 m10 m 10 m
6 m
6 m
6t/m
10t/m10t/m
/. STRUCTURI CO+BINATE
10 m 10 m
6 m
6t/m
VA= 60 t VB = 60 t
VA + VB = 6 t/m x 20 m = 120 t
VA = VB = 120 t/ 2 = 60 t
&A=&B = %2 / 8 = 6t/m x 202 / 8 x 6 =50 t
&A=&B = 50 t
&A= 50 t &B = 50 t
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VB = 60 t
&B = 50 t
10t/m
4 m 4 m
6 m