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. 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 60 3.0 tn 0.5 6.565 0.5 0.3.34 log 30 3.40 π tn 30 e exp( π tn 30 6.337 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 ( ω ( γ sin( ω sin( ω φ ( ω φ ω cotω.3 ω φ R 0 0 0.. 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

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 0.5 4.04 φ / 3 35 / 3 3.33 3

λ (tn cot ω 3.0 (tn4.04 cot ω 0.75 3.0 cot ω (m ( ω ω ( ( 4.04 γ λ 0 3.0 0 λ sinω sinω 4.04 ( ω 4.04 9.77 0λ sinω sin( ω φ sin( ω 35 sin( ω 35 ( ω φ ( ω 35 4.04 3.33 ( ω 7.37 6 66 6 λ 0.75 3.0 cot 6.4m (64.04 9.77 0.35 96.49 kn/m sin 6 sin(6 35 96.49 43.5 kn/m (6 7.37 6636465 3.. ( (m (kn/m (kn/m 6.4 96.49 43.5 6.35 93.86 43.3 63.8 9.6 43.38 64. 88.50 43.37 65.5 85.97 43.34 3.. 43.38kN/m ( sin( 43.38 sin(4.04 3.33 6.33kN/m V ( 43.38 (4.04 3.33 34.48kN/m y 3 γ 3.0 3 0 0 3.0.3m 3 γ 3 0 0 3.0 x B n.75 0.5. 3.47m y 4

3.3 3.3 tn 0.0.3 tn 6.565.0 φ / 3 30 / 3 0 ω tn h 3 0 tn 70.7 h cot tn cot 6.565 3 tn.3 ω0 70. 7 λ tn h cot ( h cot ω 3.0 tn.3.0 cot 6.565 (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 (.3 6.565 (3.0.0.0 0 λ.3 sin ω sin 6.565. λ 0kN/m γ9kn/m 3 φ30 c0 φ/3 ( ω.3 9.688 6.578 0 λ sin ω ( ω.3 55.0 0.90 0 λ (kn/m sin ω sin( ω φ sin( ω 30 sin( ω 30 ( ω φ ( ω 30.3 0 ( ω 6.3 5 56 5 λ.4 4 cot 5.73m (5.3 55.0 0.90 0. 73 45.56 kn/m sin 5 sin(5 30 45.56 55.6 kn/m (5 6.3 53545556. ( (m (kn/m (kn/m 5.73 45.56 55.6 53.6 40.4 55.34 54.5 35.04 55.38 55.40 9.94 55.5 56.30 5.03 55.05 3.4 5

. 55.38kN/m ( 54 0 70.7 hm :0. :.0 55.38kN/m λ.5m 0kN/m ω tn 6.565.0 φ / 3 30 / 3 0 ψ φ 30.3 0 6.3 γ ( h ( h γ γ 9 (3 0 (3 9.0kN/m 9 0 9 h h ( tn cot ( tn.3 cot 6.57 4.9kN/m η tn tn.3 4.9 9.0 0.03 X (tn ψ cotφ(tnψ η tnψ (tn6.3 cot30(tn6.3 0.03 tn 6.3 0.739 tn tn X 0.739 53.5 o 7.7 sin( ω φ(cotω η ( ω ψ sin(53.5 30 (cot 53.5 0.03 9.0 55.40kN/m (53.5 6.3 3m ω ο 70.7 ω 54. 3.4 3.3 tn 0.0.3 6

3.5.3 h5.0m 3.0m tn 0.0.3 tn 6.565.0 φ / 3 30 / 3 0 :0. ω tn h 5 3 0 tn 40.4 h cot tn 5 cot 6.565 3 tn.3 ω0 40. 4 6.57 ( tn φ ω ( sin( φ sin( φ ( sin( φ :.0 γ9kn/m 3 φ30 c0 φ/3 3.6 0kN/m ( 30 0.3 6.565 tn 6.565 (.3 0 sin( 30 0 sin( 30 0.3 6.565 (.3 6.565 sin( 30 6.565 43 o 40.4 K ( ( φ sin( φ sin( φ ( ( ( 30.3 sin( 30 0 sin( 30 6.565 (.3 0 (.3 6.565 0.75.3 (.3 0 K γ h5.0m 3.0m 9 3 0.75 6.kN/m :0. 6.565 :.0.3 6.kN/m 3.3 ω 0 40.4 ω 43 0kN/m. 7

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

4. 4. 0kN/m 6 87.5 tn(6 30 cot 6 95.5kN/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 ( 0 0 0.333 B.80 γ K γ 9 5.0 0 0.333 95.74kN/m 9 5.0 4. 0 0 0 ( λ cot ω 5.0 cot ω (m (3 30 K tn 45 tn 45 0.333 γ φ K 9 5.0 γ 0 0.333 95.74kN/m 9 5.0 γ cot ω λ 9 5.0 cot ω 0 5.0 cot ω 87.5cot ω (kn/m sin( ω φ sin( ω 30 87.5 cot ω 87.5 tn( ω φ cot ω (kn/m ( ω φ ( ω 30 0 0 58 6 58 87.5 tn(58 30 cot 58 95.5kN/m 59 87.5 tn(59 30 cot 59 95.76kN/m 60 87.5 tn(60 30 cot 60 95.83kN/m ( 6 87.5 tn(6 30 cot 6 95.76kN/m 9

4.3 4. 0kN/m ( ( sin 35 5 sin 35 0 sin 35 5 sin 35 5-0.085 5 0 5.0 5 ( ( sin 35 9.8 sin 35 0 sin 35 9.8 sin 35 9.8 0.000 9.8 0 5.0 9.8 γ0kn/m3 φ35 c0 9.8 4.3 5.0m B.8m 4.. ( φ sin φ sin( φ sin sinφ 0 γ 5 ( 35 5 sin 35 0 sin( 35 5 sin sin 35 0.075 5 0 5.0 5 K φ sin( φ sin φ γ K 0 5.0 γ 35 0.53 sin( 35 9.8 sin 35 9.8 9.8 0 0.53 75.9kN/m 0 5.0 ( ( sin 35 0 sin 35 0 sin 35 0 sin 35 0-0.03 0 0 5.0 0 0

4.4 4.4 K φ 30 30 35 30 0.44 φ 30 30 35 6.0m. 30 γ0kn/m 3 φ35 c0 γ 0 6.0 0. 44 59.kN/m K sin sin 30 ω 45 φ sin 45 35 30 sin 47. sin φ sin 35 sin sin 30 ω 45 φ sin 45 35 30 sin 77.8 sinφ sin 35 90 55 0 30 30 ( K ( ( φ sin( φ sin( φ ( ( 6.0m 30 59.kN/m 30 0 ( 0 30 ( 35 0 sin( 35 30 sin( 35 30 ( 0 30 ( 0 30 0.44 ω 77.8 ω 47..

4.5 4.6 ( C γ ( φ sin( φ sin φ h.8m 6.m 33.69γ0kN/m 3 φ35 c0 :.5 0kN/m 0 5(35 4. 5<<300 7.6 70 sin 35 (7.6 35 { tn(7.6 35 cot 35 tn(7.6 35 0.05}. 5.75kN/m γ ( h ( h 0 8 ( 6..8 0 ( 6.. 70kN/m γ 0 0 h h.8.8 75.6kN/m tn γ tn 33.69 0 η sin φ ψ ψ φ 75.6 0.05 70 { tnψ cotφ tnψ η } C 0 4.6 ( ψ( (kn/m C (kn/m - C 0 35 58.98 79.49 79.49 5 40 53.78 84.58 69.0 0 45 50.6 9.36 58.80 5 50 47.94 00.55 47.39 0 55 47.00 3.47 33.53 5 60 47.3 3.94 4.37 30 65 48.87 66.95-8.08 35 70 5.75 34.88-63.3 7.6 6.6 47.96 47.78 0.8.

4.6.8 50555354 4 :.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-- / 50.9 57.48 0.34.000 9.66 5.35 54.98 0.358.000 9.68 5.8 5.55 0.375 0.999 9.73 53.37 50.8 0.39 0.999 9.64 54.376 47.89 0.407 0.998 9.53 9.7kN/m 5 4.7.0m :0.5 4.8 L :.8 (0kN/m 3 35.5m 85.5 3.0 3.0.0.5 9 4.5 (kn/m tn ω tn ω sin( ω φ sin( ω 30 sin( ω 30 ( ω φ ( ω 30 0 0 ( ω 50 50555354 3. 0.5 4.0 5. 5 m.8 0.5m :.8 4.0m 3.m 4.8 γ0kn/m 3 φ35 c0 0 tn 9. 05.8 3

9. 05 K K 0 ( ( 0 9.05 ( φ sin( φ sin( φ ( ( sin φ φ ( 35 0 ( 35 9.05 sin( 35 9.05 ( 0 9.05 ( 0 9.05 9.05 9.05 35 9.05 0.4 9.05 9.05 35 γ 0 5.5 0. 4 7.7kN/m K 0.4 5 5. ( 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 (5 999 998 998 Q&05 005 3000 :0.0 400 :0.5 0kN/m N30 5. γ0kn/m 3 φ 35 c0 4

(n 0 B0.7 3kN/m 3 4.5kN/m 3 0.30.5m y 0kN/m 5kN/m 5.3 50% 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 (0.50.7 x NN>5 35 0kN/m 3 30 9kN/m 3 5.3 5 8kN/m 3. 8m 5.. γ (kn/m 3 φ ( c (kn/m 0 35 0 9 30 0 L<50% 8 5 0 0.005 0.075 0.5 0.85.0 4.75 9 75 300 (mm 5.4 3kN/m 3 4.5kN/m 3 5

N N 5. N d 30N (kn/m N d /30N (kn/m.75 3.0 0.4.75 6 0.4.75 ( 0. 0.5 0.85m ( 0 η 0kN/m. (kn/m u(kn/m N,000 900 300 900 300 300 00 00 00 0,000 0,000,000 40400 0000 3050 030 530 05 3.0m V x B.75m y ω Α. tn n tn 0.5 4. 04 φ 35 3.33 3 3 5. ( ( c 3kN/m 3 3.0 c B γ c ( ( 0.4.75 3 74.8kN/m :n :0. :n :0.5 x c B B 6 B ( n n K 4.04 0.36 ( ( φ sin( φ ( ( 4.04 3.33 sinφ (35 4.04 sin(35 3.33 sin 35 (4.04 3.33 4.04 6

0 0 3.0 γ K 0.36 γ 0 3.0 43.44kN/m ( ω tn tn 63.7 ( φ ( sin( φ sinφ sin( φ ( 35 3.33 4.04 ( 4.04 3.33 sin( 35 3.33 sin( 35 3.33 4.04 4.04 sin 35 λ (tn cot ω 3.0 (tn4.04 cot 63.7.3m γ ( ω λ sin ω (63.7 4.04 0 3.0 0.3 sin 63.7 4.04 89.9kN/m sin( ω φ sin(63.7 35 89. 9 ( ω φ (63.7 35 3.334.04 43.37kN/m V sin( 43.44 sin(4.04 3.33 6.37kN/m ( 43.44 (4.04 3.33 34.5kN/m y 3. 0.00m 3 3 x B n y.75 0.5. 00.50m 6 h. h 3 φ φ 3 h 3 h > 3 7

7 γ K K Σ 34.5kN/m M r c xc V x M y 34.5. 00 34.5kNm/m o γ K K γ K γ (3 ΣV c V 74.8 6. 37 00.55kN/m M r M o 0.6 34.5 d 0.68m ΣV 00.55 B.75 e d 0.68 0.0m 74.8 0.85 6.37.50 0.6kNm/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

5.3 (.75 e B 0. 9 m >e0.0m (O.K. 6 6 ( B.75 F t 4.38 3. 0 (O.K. e 0.0 ΣV00.55kN/m d0.68m e0.0m 96.9kN/m B.75m. 8.kN/m ( 0.6 ΣV 00.55 Fs µ 0.6.75 >.5 (O.K. Σ 34.5 (3 5 ΣV 6e 00.55 6 0.0 96.9kN/m ± ± B B.75.75 8.kN/m d 600kN/m d 600 Fs 6. > 3.0 (O.K. 96.9 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

0.7 0.6 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,500,380 00 0 kn/m γ9kn/m 3 φ30 0kN/m (kn/m 400 0 300 :.5 00 00 50 30 0 3 4 5 6 7 8 (m. : 5. (30 50 (30 50 3 90 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 0 980 0,00. 00 γ c 4.5 kn/m 3 0

(6 SD95 6. y 00,000 0 kn/m 0.0735 xc 0.7m 0.74 (. x (m (m (m x(m (m 3 0.00.380 0.038 0.3 0.006 0.98.380.354 0.60 0.850 0.98 0.00 0.0098 0.773 0.0076.376 0.834,500,380 0 o 0 980,00.. x (m (m (m x(m (m 3 0.00.380 0.380 0.050 0.0069 0.00.380 0.038 0.07 0.005 0.0 0.0 0.044 0.060 0.0009 0.980 0.00 0.0980 0.60 0.0598 0.980 0.00 0.0098 0.447 0.0044 0.740 0.0735 ( 0.74 4.5 6. 7 kn/m c 00 x.376 9 6.4kN/m s 0.834 xs 0.6m.376 (3.00 0 0.00kN/m x 0.0.00 / 0. 60 m (4 6.3 φ 30 K tn 45 tn 45 0.333 γ K 9.5 γ y 3 γ.5 3 0 9.5 0.60m 3 γ 3 0 9.5 0 0.333.kN/m 9.5

y λ0.866m 0 kn/m y 0 kn/m γ K γ 9.5 0 0.96 0.77kN/m 9.5.50m 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 30 0.00.4 9.5.4 K φ sin( φ sin φ y 30 0.96 sin( 30.4 sin 30.4.4 x 30 35 6.5 K 6.6 K V sin 0.78 sin. 4 4.kN/m 0.78. 4 9.97kN/m y φ35 φ30 γ ( 3 γ.5 3 0 9.5 0.60m 3 γ 3 0 9.5 φ35 φ30 6.5K 6.6 γ

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 6.7 0 0.7.8 0 6.4 0 0.6 5.95 0 0.00 0 0.60 6.00 0 0.00. 0.60 0 7.7 485. 3.76 7.7 ΣVx Σy 3.76 7.7 d 0.38m ΣV 4.85 B. e d 0. 38 0.7m. V x y Vx y 6.7 0 0.7.8 0 6.4 0 0.6 5.95 0 0 0 0 0 4. 9.97.0 0.60 4.5 5.98 36.96 9.97.8 5.98 ΣVx Σy.8 5.98 d 0.44m ΣV 36.96 B. e d 0. 44 0.m 3

6.3 B. e 0.8m 6 6 e0.7m<e 0.8m (OK ΣV 6e 36.96 6 0. 53.76kN/m ± ± B B.. 3.44kN/m mx 53.76kN/m < 50kN/m (O.K. 6.4 B. F t 3. 4 3.0 (OK e 0.7 e0.m<e 0.8m (OK 00 0 kn/m B. F t 5. 00 3.0 (OK e 0. 0.6 ΣV 4.85 Fs µ 0.6. >.5 (O.K. Σ. ΣV 36.96 Fs µ 0.6. >.5 (O.K. Σ 9.97 ΣV 6e 4.85 6 0.7 75.08kN/m ± ± B B...83kN/m mx 75.08kN/m < 50kN/m (O.K. h.38m 0 y. ( φ30 φ 30 0 0.0 tn 0.8 3 3.38 K ( φ sin( φ sinφ ( ( (30 0.8 0.303 sin( 30 0 sin 30 (0.8 (0.8 0 (0.8 0 4

0 9.38 γ h K 0.303 9.66kN/m γh 9. 38 ( 9.66 (0.8 0 9.03kN/m y h 3 γh.38 3 0 9.38 0.56m 3 γh 3 0 9.38 ( S 9.03kN/m M y 9.03 0. 56 5.06kNm (3,000mm d 0 50 70 mm,000 s D0@5mm 7.33 570. 6 mm 5 s 570.6 np n 5 0. d,000 70 3 S 9.03 0 τ c 0.3N/mm < s 0.39N/mm (O.K. d,000 70 (4 z.0m / z 0 γ z K 9.0 0.303 5.9kN/m γz 9. 0 5.9 (0.8 0 5.5kN/m z z y z z 3 γz.0 3 0 9.0 0.4m 3 γz 3 0 9.0 M d z z z yz 5.5 0.4.3kNm d0 z tn 50,000 tn 0.8 64 mm ( np np np k 0. 0. 0. 0.387 j 7 8 0.387 j k 0.87 3 3 6 M 5.06 0 σ c 6.N/mm < c 8.0N/mm (O.K. kjd 0.387 0.87,000 70 6 M 5.06 0 σ s 45N/mm < s 60N/mm (O.K. jd 570.6 0.87 70 s 570.6 7 M r σ s s jd z 60 64.550 6 Nmm.55kNmM z.3knm 8 ( σ s 80 l 0 φ 0 8 τ 4.6 mm 4 0 η z l d,000 8 64 655mm0.6m 0 z 5

z.0m η0.6m D0@5mm D0@5mm i50 d70 d70 i50 8@5,000 B,00m. 8@5,000 B,00m. M(kN x(m V(kN/m m/m.64 0.48.7 6.4 0.49.8 0.0 0.48 4.80 34.3 0.34.67 4.47 7. 0. x 0 kn/m 6.5 s ( c (0. 0. 0.98 4. 5.64kN/m 0.98 0. 0. xc 0.48m 3 0. 0..38m 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 0.6-0.0.49m. c S 4.47kN/m 6.(3 0.00kN/m x 0.6-0.0.48m M7.kNm/m >5.4kNm/m d 6.3(3 75.08kN/m.83kN/m 75.08.83 3 75.08 0. 67.0kN/m. ( R (.83 67.0 0. 98 34.3kN/m 0.98.83 67.0 xr 0.34m 3.83 67.0 6

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