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1 - k k k = y. k = ky. y du dx = ε ux ( ) ux ( ) = ax+ b x u() = ; u( ) = AE u() = b= u () = a= ; a= d x du ε x = = = dx dx N = σ da = E ε da = EA ε A x A x x

2 - σ x σ x = Eε x N = EAε x = EA = N = EA k = = EA. AE k = =. A E A E 6 N / mm = 6 kn / mm = A =.5 π.5 mm = π.[ m ] [ m ] = [ m] [ mm] =

3 -.5 π 6 k = = 8.89 [ N / mm] y y M( x) + x= M ( x) = x dw EI = M( x) dx = x EI δ dw dx θ EI = EI = x + C M ( x ) 6 EIw = x + Cx + C x [ C C ] x = θ () = w () = θ () = C

4 - EIθ = + C = () C = w () = EIw C 6 () = + = C = 6 = C wx ( ) = ( x x+ ) EI 6 δ x = w() = δ = EI δ = EI k y EI = = EI k =.5 yx ( = /)

5 - 5 y = 8EI 8EI k = y = EI.6 y k I b I = 5. = =.5 cm δ 5[ cm ] E = 5 = 6 kn / mm 6 N/ cm 5[ cm ] (.5).[ cm ] 5 - EI 6.5 k = = = 5.56 / 5 [ N cm]

6 - 6 = R; R= = Q+ Q R Mij + M ji Q = ( ) I I EI 6EIR 6EI Mij = M ji = ( R) = = E = Q+ Q = ( I + I) E k = = ( I+ I ).7 δ I θ = θ = R θ = θ E I I

7 - 7 EI = EI M = θ R EI M = M = θ EI M = ( θ R) = M EI M = ( θ R) = M M ( θ R) ( ) ( ) M + M = I I ( θ R) + θ = I I I R = ( + ) θ M M EI = + ( θ θ R) ij i j EI = + ( θ θ R) ji j i I θ = R I I + = Q+ Q M + M Q = I 6EI 6EI = ( θ R) = ( ) R I I + I 6I 6EI + = R I I + Q M + M = = Q

8 - 8 K H = Q I 6I EI + δ = R I I δ = + δ R = I 6I EI + K H = = δ I I.8 + K ' H I K I 6I EI + = I I + ' H I K I 6 EI + I EI = ( I ) + I ' H I K K H H EI = K EI i K = i= i k =.5 k =.5

9 - 9.5 DFc = = DFb = = ψ = X M = k = 5 M = k = 5 X = δ () R (.5) (.5) E ( ) X 87.5X Q = = X /.5

10 - 87.5X = Q= X X = 87.5 ψ ψ = X = 87.5 R ψ = RK = EI EI = EI EI KH = = =.5 I =.5 II ; = I K H I 6I EI + EI EI.5EI = I I = = = +.5 +

11 W ys =.9 k k y s y m d ( y+ y s ) m m = dt W W d ( y+ ys ) m = k( y+ y ) s + W dt y s t d y + ky = m dt m dt d y ω ; y k + = ω = m ω f T ω f =. π π T = =. f ω - K( y+ y s ) y + y s m W a) b) c)..

12 - π m π mg T = = π = ω k g k mg W cm η; η = = ; g = 98 5 k k sec. (.) y = Ccosω t+ Dsiω t.5 t = y = y y = v y = Ccos + Dsi C = y (.5) y = Cωsiωt+ Dωcosωt v = Cωsi + Dωcos v = Dω v D = ω.6 C D (.5) v y y t ω t acosθ + bsiθ = a = + + b si ( θ + α) cosω si ω.7 α = ta a b

13 - (.7) v = + si( + α) y y ωt ω α.8 y v + ω α y α = ta y v ω.9 v ω y (.) y = Ccosω t+ Dsiω t y = Cω siω t+ Dω cosω t. t = y = y y = y = Ccos + Dsi C = y Cωsi + Dωcos = Dω = ; D= C D (.) y = y cos ωt.

14 - f T W 588 k = = = 76 [ N/ m] y.5 W 588 m= = = 6[ kg] g 9.8 [ N ] [ ] kg m /sec [ N] = [ kg] m = kg m /sec /sec k 76 ω = = =. / sec m 6 ω. f = = =.[ Hz] π π T = =.9[ sec] f [ rad ] T 5 =..6 =.7 sec 5 E =.6 kn / cm I = 5 [ cm] [ ] m [ kn ] [ N ] [ kg] = = =

15 - 5 5 EI.6 k = = 6 5 = 9. / =.9 / 6 [ kn cm] [ N m] W = 98kN m T = π =. k.9 = = 6 [ ] sec W[ N] W 98 η = = =.98 6 k.9 =.98 [ cm] [ m] EI 5m T = η =..98 =..7 5 =.8 sec [ ] b D= 5 5[ cm] E =.6 kn / cm W 9[ kn] = 9[ kn ] 9 [ N ] m= = =. [ kg] I bd = = = 5. cm 5 5 [cm ] W=9 [kn] I= E=.6 [kn/cm ] 6[m] 5 5 [cm ] [m]

16 - 6 EI.6 5. k = = 6 = / =. / 5 7 [ kn cm] [ N m] m. T = π =.. 7 k = = [ ] sec W[ N] W 9 η = = =.7 7 k. =.7 [ cm] [ m] T = η =..7 = =.7 sec [ ] W=9 [kn] 6 [cm ] 5 5 [cm ] E =.6 kn / cm 7 =.6 kn / m 6[m] I I b 5 5 [cm ] E=.6 [kn/cm ] [m]

17 - 7 I I b bd 5 5 = = 5 = 5.8 cm = 5.8 m bd 6 = = 5 = 5. cm = 5. m W = 9 E = 9 [ kn] [ N ] =.6 kn / cm k =.6 7 (kn/m ) k = = =..6 [ kn m] 7 [ kn cm] [ N m] =.5 / = 5. / =.5 / (.8) I 6I EI + k = I I + m [ N ] W 9 m= = =. g 9.8 [ kg] T T π m. = = π = π =.6 sec 7 ω k.5 [ ] W[ N ] g m/sec T W 9 =. η =. =. =.5[ sec] k 5.

64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () m/s : : a) b) kg/m kg/m k

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