γ = 2(h / h 0 - 1) = 2(159,8/115,6 - 1) = 0,765;
m 1 = m 4 = P 1/(ql) = P 4/(ql) = 7,4/(14,8×18) = 0,028;
m 2 = m 3 = P 2/(ql) = 27,4/(14,8×18) = 0,103;
A = 0,5 + m 2 - α(m 1 + m 2 - m 3 - m 4) - α(m 2 - m 3) = 0,5 + m 2 = 0,5 + 0,103 = 0,603.
. 31.
K 0, , P 1 (0 ≤ K 0 ≤ α);
K 0 = (A + m 1)/[1 + γ(A + m 1)] = (0,603 + 0,028)/[1 + 0,765(0,603 + 0,028)] = 0,426 > α = 0,083.
, .
K 0, , P 1 P 2 (α ≤ K 0 ≤ α + α)
(A - 2γα m 1)/(1 + γ× A) = (0,603 - 2×0,765×0,083×0,028)/(1 + 0,765×0,603) = 0,41 < α + α = 0,413.
. 32.
,
x 0 = K 0 l = 0,41×1800 = 738 .
3. 18 1:15 (. 32).
: q = 7 /, q = 5,5 /.
: - 144 ´ 33 ( 150 ´ 40 ) .
2- , - 3- . , , / 12 . , - .
h = l /12 = 18/12 = 1,5 . ,
h 0 = h - 0,5 li = 1,5 - 0,5×18×0,0667 = 0,9 .
b = Σδ + Σδ = 4×3,3 + 2×1,2 = 15,6 .
13 l - 10δ = 152 - 1,2×10 = 140 .
.
h' 0 = h 0 - h = 0,9 - 0,144 = 0,756 ; 0,5 h' 0 = 0,378 .
x
x = = 18 = 6,9 , γ = h' 0/(li) = 0,756(18×0,0667) = 0,63.
:
hx = h 0 + ix = 0,9 + 0,0667×6,9 = 1,36 ;
h'x = 1,36 - 0,144 = 1,216 ; 0,5 h'x = 0,608 ;
hx = 1,216 - 0,144 = 1,072 ; 0,5 hx = 0,536 .
Mx = qx (l - x)/2 = 7×6,9(18 - 6,9)/2 = 268,1 ×;
( )
W = Mx γ n / R = 268,1×106×0,95/9 = 28,2×106 3;
I = W hx /2 = 28,2×106×1360/2 = 192×108 4.
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(. . 32).
, ,
I = I + I E K / E = 2[(132×1443/12) + 132×144×6082] + 2×12×13603×0,9×1,2/12 = 195,5×108 > 192×108 4;
W = I ×2/ hx = 2×195,5×108/1360 = 28,75×106 > 28,2×106 3,
K = 1,2 - , .
σ = MxE K (W E ) = 268,1×106×0,9×1,2(28,75×106) = 10,1 < R m /γ n = 14×0,8/0,95 = 11,8 .
m = 0,8 - , , , . 1,5 ,
λ y = l (0,29 b) = 150(0,29×15,6) = 33,2 < 70 , ,
φ y = 1 - a (λ/100)2 = 1 - 0,8(3,32/100)2 = 0,91,
σ = Mx / W = 268,1×106×28,75×106 = 9,32 < φ yR /γ n = 0,91×11×0,95 = 10,5 .
x 1 = 1,385 (. . 32).
M = qx 1(l - x 1)/2 = 7×1,385(18 - 1,385)/2 = 80,5 ×;
Q = q (l /2 - x 1) = 7(18/2 - 1,385) = 53,3 ;
h = 0,9 + 1,385×0,0667 = 0,99 ;
h = 0,99 - 2×0,144 ≈ 0,7 - , 0,5 h = 0,35 .
, :
I = 83×108 4;
S = 8,9×106 3.
,
σ = M ×0,5 h / I = 80,5×106×350/83×108 = 3,4 ;
τ = QS /(I Σδ) = 53,3×103×8,9×106/(83×108×2×12) = 2,4 .
II-25-80 (45)
0,5σ + = 0,5×3,3 + = 4,56 < (R α/γ n) m = (5,7/0,95)0,8 = 4,8
α = 0,5arctg (2τ/σ) = 0,5arctg (2×2,4/3,3) = 27,5
. 17 ( II-25-80, . 5).
: a = 1,3 ( ); x 2 = 0,7 ;
h = (0,9 + 0,7×0,0667) - 2×0,144 ≈ 0,66
h /δ = 660/12 = 55 > 50; γ = a / h = 1,3/0,66 ≈ 2.
. 18 19 . 5 γ = 2 K = 15 K τ = 2,5.
x 2,
I = 74×108 4; S = 8,4×106 3.
M = qx 2(l - x 2)/2 = 7×0,7(18 - 0,7)/2 = 42,4 ×;
Q = q (l /2 - x) = 7(18/2 - 0,7) = 58,1 .
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σ = M 0,5 h / I = 42,4×106×0,5×660/74×108 = 1,9 ;
τ = QS /(I Σδ) = 58×103×8,4×106/(74×108×2×1012) = 2,75 .
II-25-80 (48) :
)
σ/[ K (100δ/ h )2] + τ/[ K τ(100δ/)2] = 1,9/[15(100/55)2 + 2,75/[2,5(100/55)2] = 0,38 < 1, h /δ = 55;
) (x = 6,9 ) h /δ = 1,21/0,012 = 101 > 50;
γ = a / h = 1,3/1,22 = 1,07, K = 20 K τ = 3,5.
σ = Mx 0,5 h / I = 268,1×106×536/181×108 = 7,9 ,
I = 181×108 4;
τ = QxS /(I Σδ) = 14,7×103×12,8×106/(181×108×2×12) = 0,43 ,
Q = q (l /2 - x) = 7(18/2 - 6,9) = 14,7 ,
S = 12,8×106 3.
II-25-80, (48),
7,9[20(100/101)2] + 0,43[3,5(100/101)2] = 0,53 < 1.
II-25-80, . 4.27 4.29.
, ,
I = 65,5×108 4; S = 9,1×106 3;
τ = QmaxS /(I Σδ) = 7,9×103×9,1×106/(65,5×108×2×12) = 3,65 < R /γ n = 6/0,95 = 6,3 ;
τ = QmaxS /(I nh ) = 7,9×103×9,1×106/(65,5×108×4×144) = 0,15 < R /γ n = 0,8/0,95 = 0,84 .
. 4.33 (50) II-25-80. :
f = f 0[1 + c (h / l)2]/ ,
f 0 = 5 q l 4(384 El) = 5×5,5×1012(384×248×1012) = 30 .
EI = E I + E I = 104×175×108 + 104×0,9×1,2×67,5×108 = 248×1012 ×2 ( II-25-80, . 4, . 3); = 0,4 + 0,6β = 0,4 + 0,6×900/1500 = 0,76 c = (45,3 - 6,9β)γ = (45,3 - 6,9×900/1500)2×144×132[2×12(1500 - 144)] = 48,1;
f = 30[1 + 48,1(1,5×103/18×103)2]/0,76 = 53 f / l = 53/18×103 = 1/340 < 1/300 ( II-25-80, . 16).
. 33.
4. 5,8 , 3 (. 33). , i = 0,1. - III ( ).
II-6-74 III α ≤ 25 c = 1 P = 1 /2.
K = 12,
(g 1 + P )/[1000/(K l) - 1] = (0,3 + 1)/[1000/(12×5,8) - 1] = 0,1 ×2.
:
0,06 /2; 3 (0,03 ´ 1,0 ´ 1,0)6 = 0,18 /2; 8 ´ 12 (0,08×0,12×1,0)6 = 0,06 /2; 0,3 /2.
1 :
q = (g 1 + g + P ) B = (0,3 + 0,1 + 1)3 = 4,2 /, 1,2 /; 3 /;
q = [(g 1 + g ) n 1 + P n ] B = [(0,3 + 0,1)1,1 + 1×1,6]3 = 6,12 /, n 1 = 1,1 n = 1,6.
, II-6-74.
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M = ql 2/8 = 6,12×5,82/8 = 25,73 ×;
Q = ql /2 = (6,12×5,8/2) = 17,75 .
15 . 2- , II-25-80, . 3.1 3.2. m γ n, 384-76.
R = R = 15 m /γ n = 15×0,9/0,9 = 15 .
(17) II-25-80.
W = W K ω = 0,9 bh 2/6 = 0,9×150×3002/6 = 2,03×106 3, K ω = 0,9 II-25-80, . 13.
M / W = 25,73×106/2,03×106 = 12,7 < 15 , .. .
. , b = 150 , : δ = 12 , b = 150 , l = 58 , h = 30 .
S = 3,5 h + δ = 3,5×30 + 12 = 117 ≈ 120 .
(58), II-25-80 m
T = 0,75 b m = 0,75×15×0,9 = 10,12 .
- 0,2 l = 0,2 ´ 600 = 120 .
0,4 l (45):
n ≥ 1,2 MS /(l T) = 3×1,2×25,73×106(2×300×10,12×103) = 15,3 ≈ 16 .
, 0,4 l 12
n = 0,4 lS = 0,4×580×12 = 19,3 > 16.
f = 5 q l 4/(384 EIK ) = 5×4,2×5,84×1012/(384×104×3,375×108×0,75) = 24,4
f / l = 24,4/5800 = 1/238 < 1/200, .. .
50 d = 16 .
f = 1,5 f = 1,5×24,4 = 37 .
6.26. . , . 1.
II-25-80, . 6.21 6.24.
( ) . 12 .
. , , .
. , .
6.27. . () ; , , () - .
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0,75 /2 . .
6.28. , , . 4.14 - 4.16 II-25-80, . 3.5.
6.29. e ,
E' = Nsi > N;
E' = Nsi ≈ N,
E' = 300 R II-25-80, . 3.5.
F - ;
N - ;
Nsi - ;
l - ;
δ i - . 21;
m - .
m = 1; m = 2; m = 2, m = 4.
6.30. , , II-25-80 . 4 .
6.31. , () , 25 % 40 % - .
6.32. .
II-25-80, . 4.16.
; , .
. M ,
M = Δ Ne,
Δ N - , ;
e - .
6.33. - II-25-80, . 4.17 4.18, , - - . 4.2 4.6 . 6.21 .
6.34. .
M M () :
q
M = ql 2 n /14 - 0,64 Nf;
M = - ql 2 n /10 + 0,72 Nf;
P
M = Pln /6 - 0,56 Nf;
M = - Pln /6 + 0,88 Nf.
:
M = ql 2 n /24 - Nf /3;
M = - ql 2 n /12 + 2 Nf /3;
M = Pln /8 - Nf /4;
M = - Pln /8 + 3 Nf /4,
ln - ;
N - ;
f = l 2 n /(8 r) - , ln r, .
r = (l 2 + 4 h 2)/(8 h),
h - , l - .
6.35.
M = M 0 - Nf,
M 0 - l;
N - ;
f - .
6.36. II-25-80, . 4.21 6.23.
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1. 18 , 3 18 ´ 60 .
- . .
i = 25 %.
, .
h = 1/6 l = 18/6 = 3 . α = arctg 0,25 = 14.
h = h - (l tg α/2) = 3 - 18×0,25/2 = 0,75 .
1,075 . 6,5 .
8- (. 34).
1 2 : - 0,294 /2; - 0,323 /2.
. 34.
. (III ) P 0 = 1 /2 ; , II-6-71, . 5.5, . 5. c = 1,
P = P 0 c = 1×1 = 1 /2.
. 2
g = (g + P )[1000/(K l) - 1] = (0,294 + 1)[1000/(5×18) - 1] = 1,294/10,1 = 0,128 /2;
g = 0,128×1,1 = 0,141 /2.
,
(g + g )/ P 0 = (0,194 + 0,128)/1 = 0,422
II-6-74, . 5.7 n = 1,59, 1 2
P = P 0 Cn = 1×1×1,59 = 1,59 /2.