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1 0 ( L CONTENTS 0

2 . sin(-x-sinx, (-x(x, sin(90-xx,(90-xsinx sin(80-xsinx,(80-x-x ( sin{90-(ωφ}(ωφ. :n :m.0 m.0 n tn. 0 n.0 tn ω m :n.0n tn n.0 tn.0 m c ω sinω c ω c tnω ecω sin ω ω sin c ω c ω tn c tn ω rctnω tnω secω ω (/c (/c (/ c cotω tn ω.3 tn 60 (tn tn log π tn 30 e exp( π tn c B C sin sin B c sin C sin sin c sin B sin C ε c 90ε sin(90 ε ε c

3 . (3 ( ω ( γ sin( ω sin( ω φ ( ω φ ω cotω.3 ω φ R λ ω λ h ω ( ( ω γ λ sin ω λ (tn cotω ( γ ( ω ( ( h h λ sinω sin λ tn h cot ( h cotω h ω Α :m :n ω Α :m :n tn ω η tn ( φ ( sin ( φ sin φ sin( φ φ 0 ω 45 ω tn (tn ψ cot φ (tn ψ η tn ψ ψ φ γ ( h ( h γ h h ( tn cot γ ( tn φ ω ( sin ( φ sin( φ ( sin( φ ω Α

4 3 (3 3. :m ( γ K γ K ω tn ( ( φ sin( φ sin φ ( ( φ ( sin( φ sin φ sin( φ :n φ 3 tn n ω Α K K γ ( ( φ sin( φ sin( φ ( ( ( tn φ ω ( sin( φ sin( φ ( sin( φ 3. :n φ 3 tn n tn m ω Α 3. ( 0kN/m sin φ ψ { tnψ cotφ tnψ η } sin( ω φ(cotω η ( ω ψ ψ φ η tn γ γ h h γ ( h ( h ( tn cot h :m :n φ 3 tn n tn m ω Α 3.00m x :0.5 B.75m. y γ0kn/m 3 φ35 c0 φ/3 ω tn (tnψ cotφ(tnψ η tnψ n tn tn φ / 3 35 /

5 λ (tn cot ω 3.0 (tn4.04 cot ω cot ω (m ( ω ω ( ( 4.04 γ λ λ sinω sinω 4.04 ( ω λ sinω sin( ω φ sin( ω 35 sin( ω 35 ( ω φ ( ω ( ω λ cot 6.4m ( kn/m sin 6 sin( kn/m ( ( (m (kn/m (kn/m kN/m ( sin( sin( kN/m V ( ( kN/m y 3 γ m 3 γ x B n m y 4

6 tn tn φ / 3 30 / 3 0 ω tn h 3 0 tn 70.7 h cot tn cot tn.3 ω λ tn h cot ( h cot ω 3.0 tn.3.0 cot (3.0.0 cot ω.4 4 cot ω (m hm 3m γ ( ω ( ( h h λ sin ω sin :0. :.0 9 ( ω.3 ( ( λ.3 sin ω sin λ 0kN/m γ9kn/m 3 φ30 c0 φ/3 ( ω λ sin ω ( ω λ (kn/m sin ω sin( ω φ sin( ω 30 sin( ω 30 ( ω φ ( ω ( ω λ.4 4 cot 5.73m ( kn/m sin 5 sin( kn/m ( ( (m (kn/m (kn/m

7 kN/m ( hm :0. : kN/m λ.5m 0kN/m ω tn φ / 3 30 / 3 0 ψ φ γ ( h ( h γ γ 9 (3 0 (3 9.0kN/m h h ( tn cot ( tn.3 cot kN/m η tn tn X (tn ψ cotφ(tnψ η tnψ (tn6.3 cot30(tn tn tn tn X o 7.7 sin( ω φ(cotω η ( ω ψ sin( (cot kN/m ( m ω ο 70.7 ω tn

8 3.5.3 h5.0m 3.0m tn tn φ / 3 30 / 3 0 :0. ω tn h tn 40.4 h cot tn 5 cot tn.3 ω ( tn φ ω ( sin( φ sin( φ ( sin( φ :.0 γ9kn/m 3 φ30 c0 φ/ kN/m ( tn (.3 0 sin( 30 0 sin( ( sin( o 40.4 K ( ( φ sin( φ sin( φ ( ( ( 30.3 sin( 30 0 sin( (.3 0 ( (.3 0 K γ h5.0m 3.0m kN/m : : kN/m 3.3 ω ω 43 0kN/m. 7

9 4 4. ( γ K γ tn φ K 45 φ ω ω ω ω 45 ( γ K γ φ K sin( φ sinφ ω ω ( φ sin φ sin( φ sin sinφ 0 γ (4 h ω ω sin φ ψ tnψ cotφ tnψ η ψ φ η { } γ ( h ( h γ h h tn γ 0 C C γ ( φ sin( φ sin φ (3 γ K K φ φ ω ω ω 45 φ sin ω 45 φ sin sin sin φ sin sin φ 8

10 kN/m tn(6 30 cot kN/m 95.83kN/m ( ( K ( ( φ sin( φ sin( φ ( ( 5.00 γ9kn/m 3 φ30 c0 0 ( 0 0 ( 30 0 sin( 30 0 sin( 30 0 ( 0 0 ( B.80 γ K γ kN/m ( λ cot ω 5.0 cot ω (m (3 30 K tn 45 tn γ φ K γ kN/m γ cot ω λ cot ω cot ω 87.5cot ω (kn/m sin( ω φ sin( ω cot ω 87.5 tn( ω φ cot ω (kn/m ( ω φ ( ω tn(58 30 cot kN/m tn(59 30 cot kN/m tn(60 30 cot kN/m ( tn(6 30 cot kN/m 9

11 kN/m ( ( sin 35 5 sin 35 0 sin 35 5 sin ( ( sin sin 35 0 sin sin γ0kn/m3 φ35 c m B.8m 4.. ( φ sin φ sin( φ sin sinφ 0 γ 5 ( 35 5 sin 35 0 sin( 35 5 sin sin K φ sin( φ sin φ γ K γ sin( sin kN/m ( ( sin 35 0 sin 35 0 sin 35 0 sin

12 K φ φ m. 30 γ0kn/m 3 φ35 c0 γ kN/m K sin sin 30 ω 45 φ sin sin 47. sin φ sin 35 sin sin 30 ω 45 φ sin sin 77.8 sinφ sin ( K ( ( φ sin( φ sin( φ ( ( 6.0m kN/m 30 0 ( 0 30 ( 35 0 sin( sin( ( 0 30 ( ω 77.8 ω 47..

13 ( C γ ( φ sin( φ sin φ h.8m 6.m 33.69γ0kN/m 3 φ35 c0 :.5 0kN/m 0 5( << sin 35 ( { tn( cot 35 tn( }. 5.75kN/m γ ( h ( h 0 8 ( ( kN/m γ 0 0 h h kN/m tn γ tn η sin φ ψ ψ φ { tnψ cotφ tnψ η } C ( ψ( (kn/m C (kn/m - C

14 :.5.0m(9kN/m 3 30 /3.0m 0.5m :.5 γ9kn/m 3 φ30 c0 ω(. tnω (kn/m sin(ω-φ (ω-φ-- / kN/m m : L :.8 (0kN/m m (kn/m tn ω tn ω sin( ω φ sin( ω 30 sin( ω 30 ( ω φ ( ω ( ω m.8 0.5m :.8 4.0m 3.m 4.8 γ0kn/m 3 φ35 c0 0 tn

15 9. 05 K K 0 ( ( ( φ sin( φ sin( φ ( ( sin φ φ ( 35 0 ( sin( ( ( γ kN/m K ( 3.00 m L0m ( γ0 kn/m 3 φ35 (3 σ ck 8 N/mm γc3 kn/m 3 B750 (4 N 0 d 600kN/m ( Q& : :0.5 0kN/m N30 5. γ0kn/m 3 φ 35 c0 4

16 (n 0 B0.7 3kN/m 3 4.5kN/m m y 0kN/m 5kN/m % 50% 0.075mm o :n :n γ90kn/m 3 φ3035 c0 50% 50% 50% 50% 50% 50% D f 0.5 o 0.3m 0 B ( x NN>5 35 0kN/m kN/m kN/m 3. 8m 5.. γ (kn/m 3 φ ( c (kn/m L<50% (mm 5.4 3kN/m 3 4.5kN/m 3 5

17 N N 5. N d 30N (kn/m N d /30N (kn/m ( m ( 0 η 0kN/m. (kn/m u(kn/m N, ,000 0,000, m V x B.75m y ω Α. tn n tn φ ( ( c 3kN/m c B γ c ( ( kN/m :n :0. :n :0.5 x c B B 6 B ( n n K ( ( φ sin( φ ( ( sinφ ( sin( sin 35 (

18 γ K 0.36 γ kN/m ( ω tn tn 63.7 ( φ ( sin( φ sinφ sin( φ ( ( sin( sin( sin 35 λ (tn cot ω 3.0 (tn4.04 cot m γ ( ω λ sin ω ( sin kN/m sin( ω φ sin( ( ω φ ( kN/m V sin( sin( kN/m ( ( kN/m y m 3 3 x B n y m 6 h. h 3 φ φ 3 h 3 h > 3 7

19 7 γ K K Σ 34.5kN/m M r c xc V x M y kNm/m o γ K K γ K γ (3 ΣV c V kN/m M r M o d 0.68m ΣV B.75 e d m kNm/m 0kN/m x.50m x c 0.85m V 6.37kN/m 43.44kN/m 34.5kN/m c 74.4kN/m y.00m Σ34.5kN/m e0.0m d0.68m B/0.875m ΣV00.55kN/m B.75m. M M r o ΣV d 0 M r M d ΣV B 5.7 e d o M r M o ΣΗ d e B/ ΣV B. 8

20 5.3 (.75 e B 0. 9 m >e0.0m (O.K. 6 6 ( B.75 F t (O.K. e 0.0 ΣV00.55kN/m d0.68m e0.0m 96.9kN/m B.75m. 8.kN/m ( 0.6 ΣV Fs µ >.5 (O.K. Σ 34.5 (3 5 ΣV 6e kN/m ± ± B B kN/m d 600kN/m d 600 Fs 6. > 3.0 (O.K d e0 e<b/6 eb/6 e >B/6 db ΣV ΣΗ ΣV d e ΣΗ B ΣV Σ V e B B B Σ V e B B ΣV d e 3dB ΣΗ V Σ B 0. ΣV d e ΣΗ 3d Σ V 3 d B > e 6 B 3 e > 9

21 µ Σ V 0.5 m ΣV F s.5(. Σ D 0.5 f F S Σ γ D f K µv B (. K tn φ 45 6L 6. ( L (.50 m,500, kn/m γ9kn/m 3 φ30 0kN/m (kn/m : (m. : 5. (30 50 ( kn/m 96.8kN/m 300 ( 0 kn/m (3 γ9 kn/m 3 φ30 (4 50kN/m (5 σ ck 4 N/mm , γ c 4.5 kn/m 3 0

22 (6 SD95 6. y 00,000 0 kn/m xc 0.7m 0.74 (. x (m (m (m x(m (m ,500,380 0 o 0 980,00.. x (m (m (m x(m (m ( kn/m c 00 x kN/m s xs 0.6m.376 ( kN/m x / m (4 6.3 φ 30 K tn 45 tn γ K 9.5 γ y 3 γ m 3 γ kN/m 9.5

23 y λ0.866m 0 kn/m y 0 kn/m γ K γ kN/m m o ω 60 ω y x B.0m ω 45 φ.50m o B.0m.. (6. ( φ sinφ sin( φ sin sinφ 0. γ.4(6. ( 30.4 sin 30 0 sin( 30.4 sin sin K φ sin( φ sin φ y sin( 30.4 sin x K 6.6 K V sin 0.78 sin. 4 4.kN/m kN/m y φ35 φ30 γ ( 3 γ m 3 γ φ35 φ30 6.5K 6.6 γ

24 x B.0m (5 3 ω. p K(γ (6. sin( ω φ. ( ω φ 6.7 (6.3 γ tn. tn ω (6.(6.3(6.4 γ K. (6.5 d p K( γ. d (6.5. V x y Vx y ΣVx Σy d 0.38m ΣV 4.85 B. e d m. V x y Vx y ΣVx Σy d 0.44m ΣV B. e d m 3

25 6.3 B. e 0.8m 6 6 e0.7m<e 0.8m (OK ΣV 6e kN/m ± ± B B kN/m mx 53.76kN/m < 50kN/m (O.K. 6.4 B. F t (OK e 0.7 e0.m<e 0.8m (OK 00 0 kn/m B. F t (OK e ΣV 4.85 Fs µ 0.6. >.5 (O.K. Σ. ΣV Fs µ 0.6. >.5 (O.K. Σ 9.97 ΣV 6e kN/m ± ± B B...83kN/m mx 75.08kN/m < 50kN/m (O.K. h.38m 0 y. ( φ30 φ tn K ( φ sin( φ sinφ ( ( ( sin( 30 0 sin 30 (0.8 (0.8 0 (

26 γ h K kN/m γh ( 9.66 ( kN/m y h 3 γh m 3 γh ( S 9.03kN/m M y kNm (3,000mm d mm,000 s mm 5 s np n 5 0. d, S τ c 0.3N/mm < s 0.39N/mm (O.K. d, (4 z.0m / z 0 γ z K kN/m γz ( kN/m z z y z z 3 γz m 3 γz M d z z z yz kNm d0 z tn 50,000 tn mm ( np np np k j j k M σ c 6.N/mm < c 8.0N/mm (O.K. kjd , M σ s 45N/mm < s 60N/mm (O.K. jd s M r σ s s jd z Nmm.55kNmM z.3knm 8 ( σ s 80 l 0 φ 0 8 τ 4.6 mm 4 0 η z l d, mm0.6m 0 z 5

27 z.0m η0.6m i50 d70 d70 i50 B,00m. B,00m. M(kN x(m V(kN/m m/m x 0 kn/m 6.5 s ( c ( kN/m xc 0.48m m 0.m x s x c 0.0m c 3 x R R 0. L0.98m.40m B.0m 6.( s 6.4kN/m x s m. c S 4.47kN/m 6.(3 0.00kN/m x m M7.kNm/m >5.4kNm/m d 6.3( kN/m.83kN/m kN/m. ( R ( kN/m xr 0.34m

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