l = 60 f = 11
r = (l 2 + 4 f 2)/(8 f) = (602 + 4×112)/(8×11) = 46,41 ;
α
cos α = (r - f)/ r = (46,41 - 11)/46,41 = 0,763,
α = 4016 '. 2α = 8032 ',
S = (π r ×2α)/180 = (3,14×46,41×80,54)/180 = 65,2 .
y M
,
= r - f = 46,41 - 11 = 35,41 . 26.
26
, | ||||||||
x | ||||||||
y | 3,69 | 4,9 | 6,47 | 8,51 | 9,91 | 10,73 | ||
φ | 4015 ' | 3236 ' | 2651 ' | 2530 ' | 1851 ' | 1227 ' | 612 ' |
1 2 n II-6-74, . 2.2. k = S / l = 64,4/60 = 1,07, .
III P 0 = 1 /2 ; c 1, , II-6-74, . 5, . 5.5 :
c 1 = l /(8 f) = 60/(8×11) = 0,682;
P = P 0× c 1 = 1×0,682 = 0,682 /2.
. 2
g = (g + P )/[1000/(K l) - 1] = (0,594 + 0,682)/[1000/(4×60) - 1] = 1,276/3,16 = 0,404 /2.
. 27. g = 0,998 /2 .
g / P 0 = 0,998/1 = 0,998; n = 1,41 ( II-6-74), 1 2
P 1 = P 0 nc 1 = 1×1,41×0,682 = 0,962 /2.
27
, /2 | n | , /2 | |
0,187 | 1,1 | 0,206 | |
0,364 | 1,2 | 0,437 | |
0,043 | 1,1 | 0,047 | |
0,404 | 1,1 | 0,444 | |
- | - | 0,03 | |
0,998 | - | 1,164 |
, , c 2 = (2 + 2,2)/2 = 2,1
P 2 = P 0 nc 2 = 1×1,41×2,1 = 2,90 /2.
, 1 6 , :
. 27
q = 1,164×6 = 7 /;
P 1 = 0,962×6 = 5,8 /;
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P 2 = 2,96×6 = 17,8 /.
. 43.
1) , ; 2) , , 3) , ( II-6-74, . 5.3)
10 /:
. 43. ,
) :
V = V = l /2 = 60/2 = 300 ;
H = l 2/(8 f) = 602/(8×11) = 410 ;
) ():
:
V = 3 l /8 = 3×60/8 = 225 ;
V = l /8 = 60/8 = 75 ;
H = l 2/(16 f) = 602/(16×11) = 205 ;
) ():
V = 5 l /24 = 5×60/24 = 125 ;
V = l /24 = 60/24 = 25 ;
H = l 2/(48 f) = 602/(48×11) = 68,2 .
Mx, Qx Nx (. ) 0 ≤ x ≤ l /2 (. ) :
Mx = V × x - x 2/2 - H × y;
Qx = - H sin φ + (V - x)cos φ;
Nx = H cos φ + (V - x)sin φ.
l /2 ≤ x ≤ l - :
Mx = V (l - x) - Hy;
Qx = H sin φ - V cos φ;
Nx = - H cos φ - V sin φ.
( . )
0 ≤ x ≤ l /2:
Mx = V [ x - 3,2(l - x) x 2/ l 2] - Hy;
Qx = V [1 - 4,8(l - x) x 2/ l 2]cos φ - H sin φ;
Nx = H cos φ + V [1 - 4,8(l - x) x 2/ l 2]sin φ;
l /2 ≤ x ≤ l:
Mx = V (l - x) - Hy;
Qx = H sin φ - V cos φ;
Nx = - H cos φ - V sin φ.
. 44 . , , 1, 2 3. . 45 1, 2 3. V V H 384, 384, 523 ( 1); 341, 254, 406 ( 2) 433, 255, 408 ( 3).
, 3 , . x = 10 , - x = 50 .
M 10 = 343 ×; N 10 = -461 ; M 50 = -477 ×; M 50 = -449 .
. 44.
) ( ); ) , ; ) , ; ) , ; 1 - () (); 2 - () (); 3 - () ()
. 45. (N) (Q)
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1 - () (); 2 - () (); 3 - () ()
II-25-80, . 4.17, (28):
N / F + M / W ≤ R .
h / b = β,
h 3 - β Nh / R - 6β M /(ξ R ) = 0. (47)
(47)
h 3 + 3 ph + 2 q = 0, (48)
p = -β N /(3 R );
q = -3β M /(ξ R );
β = 5 ¸ 6;
ξ = 0,5 ¸ 0,8;
R - . 3.1 3.2 384-76.
q >> p, (48) = q 2 + p 2 > 0 . , h = U + V,
;
, 1- 4,2 . γ n = 1.
(1/40 - 1/50) l = = (1/40 - 1/50)6000 = 150 - 120 .
. 3.1 3.2, h > 120 , δ = 4,2 rk / a = 4641/4,2 = 1105 > 500 m = 0,8, m = 0,95, m = 1;
R = R = 0,8×0,95×1,0×16/1,0 = 12,2 .
(47). β = h / b = 5,5; ξ = 0,65 h = 1285 b = 1285/5,5 = 234 ≈ 240 .
b ´ h = 240 ´ 1344 32 42 .
II-25-80, . 4.17, (28).
II-25-80, . 4.4 6.25, (9):
λ = l 0/ r = 0,58 S / = 0,58 S / = 0,58 S /(0,29 h) = 0,58×65,2/(0,29×1,344) = 97.
. 6.27, ξ N (30), . 4.17, II-25-80 N 30 = 408 - (. . 45):
ξ = 1 - λ2 N 30/(AR F ) = 1 - 972×408×103/(3000×12,2×240×1344) = 0,675;
M = M /ξ = 447/0,675 = 662 ×;
W = 6 h 2/6 = 240×13442/6 = 72,253×106 3.
(28) II-25-80, :
N / F + M / W = 449000/322600 + 662×106/72,253×106 = 1,4 + 9,2 = 10,6 < 12,12 ,
.. .
(33) . 4.18 II-25-80.
150 ,
l = 2×150 < 140× b 2/(hm ) = 140×242/(134,4×0,8) = 750 ,
.. , - , , n = 1 (33), II-25-80.
:
) φ (23), . 4.14, II-25-80 m . 4.25 :
φ = 140 b 2 K /(l hm ) = 140×242×1,13/(3260×131,4×0,8) = 0,26.
II-25-80, . 4.14, φ K K . m > 4 K = 1
K = 0,142 l / h + 1,76 h / l + 1,4α = 142×3260/134,4 + 1,76×134,4/3260 + 1,4×0,702 = 4,5;
φ K = 0,26×4,5 = 1,17;
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) φ II-25-80, . 4.3, (8)
φ = A /λ2 y = 3000[(0,5 S /(0,29 b)2] = 3000×0,292×242/(0,5×65202) = 0,014.
II-25-80, . 4.18, φ K N, m > 4 :
K N = 0,75 + 0,06(l / h)2 + 0,6α l / h = 0,75 + 0,06(3260/134,4)2 + 0,6×0,702×3260/134,1 = 46,27;
φ K N = 0,014×46,27 = 0,6648.
(33) II-25-80,
N /(F φ R ) + M /(W φ R ) = 449×103/(322×103×0,6448×12,2) + 662×106/(72,253×106×1,17×12,2) = 0,18 + 0,65 = 0,83 < 1.
, .
(. 46)
N = 649 , Q = 66 (. . 45).
, 32 380-71 . 50 5 8732-78 .
(64), . 5.38, II-23-81
F /(1,25 rl) ≤ Rl γ;
r = F /(1,25 lRl v ) = 649×103(1,25×160×168×1) = 19,4 .
. 46.
1 - ; 2 - ; 3 - ; 4 - ; 5 - ; 6 - ; 7 - ; 8 - ; 9 -
d = 40 . d = 50 5 .
. R = R = R = 12,2 ;
F = N / R = 649×103/12,2 = 5,32×104 2,
b = 210
l ≥ F / b = 5,32×104/240 = 222 , l = 400 .
, 200 400 . , (. . 46).
F = 200×400 = 8×104 ;
σ = 649×103/8×104 = 8,1 < 12,2 ;
F = (2×4 + 12)δ = 20δ;
δ = N /(20 Rl v ) = 649×103/(20×168×1) = 19,3 .
20 . , , 200 ´ 160 . (. .., .., .. -. , 1963, . 192) M = 0,085 ql 2 = 0,085×8,1×1602 = 1,76×104 ×.
W = δ2/6 = M / R = 1,76×104/220 = 80 3,
δ = = = 21,9 .
22 .
,
q = Nb / F = 649×103×200/(750×200) = 865 /.
x :
W = M /(1,2 R ) = 200×222/6 = 865 x 2/(1,2×2 R ),
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x = = 99 .
,
a = 750 - 2×99 = 552 ≈ 600 .
, , , :
N = Q (15 + 2,2 + 17,8/3)/75 = 66×23/75 = 20,24 .
, II-25-80, . 5.16:
T = n 2,5 d 2 = N , n = 2;
d = = = 2,01 .
20 .
(. 47)
300 ´ 200 . , N = 52,5 .
σ = N / F = 525×103/(300×200) = 8,8 < 12,2 .
. 47.
1 - ; 2 - ; 3 - ; 4 - ; 5 - ; 6 -
,
q = 52,5/0,3 = 1750 /;
M = 1750×0,1352/2 = 16 ×.
( )
W = M /(R ×1,2) = 16×106/(220×1,2) = 60,6×103 3.
δ = = = 43 .
45 .
.
M = Q ×50 = 44×103×50 = 220×104 ×;
W = 220×104/(220×1,2) = 8,3×103 3;
b = 100
δ = = 22,3 .
δ = 30 .
, . , .
, ,
q = 525×103/750 = 700 /,
750 - 2×110 = 530 ≈ 540 .
2. .
, l = 24 , f = 6 > l /6 4,5 , (. 48). III I .
1,5 , . -1750.
, 22,5 , . , .