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Effective static loading distributions

Effective static loading distributions. Wind loading and structural response Lecture 13 Dr. J.D. Holmes. Effective static loading distributions. Static load distributions which give correct peak load effects under fluctuating wind loading. Separately calculate e.s.l.d  s for :

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Effective static loading distributions

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  1. Effective static loading distributions Wind loading and structural response Lecture 13 Dr. J.D. Holmes

  2. Effective static loading distributions • Static load distributions which give correct peak load effects under fluctuating wind loading • Separately calculate e.s.l.d  s for : • mean component • background component • resonant components • Generally e.s.l.d. s depend on load effect (e.g. bending moment, shear)

  3. Effective static loading distributions Influence coefficient : Value of a load effect as a unit load is moved around a structure :

  4. Effective static loading distributions Influence coefficient : Value of a load effect as a unit load is moved around a structure :

  5. Effective static loading distributions Influence coefficient : Value of a load effect as a unit load is moved around a structure :

  6. Effective static loading distributions Influence coefficient : Value of a load effect as a unit load is moved around a structure :

  7. Effective static loading distributions Influence coefficient : Value of a load effect as a unit load is moved around a structure :

  8. Effective static loading distributions Influence coefficient : Value of a load effect as a unit load is moved around a structure :

  9. Effective static loading distributions Influence coefficient : Value of a load effect as a unit load is moved around a structure :

  10. Effective static loading distributions Influence coefficient : Value of a load effect as a unit load is moved around a structure :

  11. Effective static loading distributions Influence coefficient : Value of a load effect as a unit load is moved around a structure :

  12. Effective static loading distributions Influence coefficient : Value of a load effect as a unit load is moved around a structure :

  13. z For a distributed load p(z) , r = Effective static loading distributions Influence coefficient : Value of a load effect as a unit load is moved around a structure : Ir(z)

  14. Effective static loading distributions Mean component  p(z) = [0.5 aUh2] Cp on a tower :  f (z) = [0.5 a U(z)2] Cd b(z) (per unit height)

  15. Effective static loading distributions Background (quasi-static) component (Kasperski 1992) pr(z) : correlation coefficient between the fluctuating load effect, and the fluctuating pressure at position, z

  16. Effective static loading distributions Background (quasi-static) component Consider a load effect r with influence line Ir(z): Instantaneous value of r : r(t) = p(z,t) = fluctuating pressure at z L is length of the structure Mean value of r :

  17. Effective static loading distributions Background (quasi-static) component Standard deviation of r : (background) (Lecture 9) Expected maximum value of r : Distribution for maximum response : pB(z) = gBpr (z) p (z)

  18. Effective static loading distributions Background (quasi-static) component Check :

  19. Effective static loading distributions Background (quasi-static) component Discrete form of pr : This form is useful when using using wind-tunnel data obtained from area-averaging over discrete measurement panels Standard deviation of load effect :

  20. h 22.5 2 1 Effective static loading distributions Example (pitched free roof) : (Appendix F in book)

  21. Correlation coefficient = -0.17 -0.60, (0.20) +0.46, (0.35) mean,std.dev. Cp’s +0.03, (-1.90) +2.53, (-0.65) peak Cp’s Effective static loading distributions Wind-tunnel test results :

  22. qh is the reference mean dynamic pressure at roof height Effective static loading distributions Mean drag force : Influence coefficients :Panel 1 : +h Panel 2 : -h Mean drag force :D = (0.46) qh (+h) + (-0.60) qh (-h) = 1.06 qh (h)

  23. qh is the reference mean dynamic pressure at roof height Peak drag force : = 1.06 qh h + 4 0.432 qh h = 2.79 qh h Effective static loading distributions Standard deviation of drag force : • D = qh [(0.35)2 (+h)2+ (0.20)2(-h)2 + 2(-0.17).(0.35) (0.20)(+h)(-h)]1/2 = 0.432 qh h assuming a peak factor g of 4

  24. [ .(h) + (-h)] = qh2 h [(0.35)2 - (-0.17)(0.35)(0.20)] = qh [Cp1 + g p1,DCp1] = qh [(0.46) + 4 (0.886) (0.35)] = 1.70 qh Effective static loading distributions Effective pressures for maximum drag force : • Covariance between p1(t) and drag D(t) : = (0.134) qh2 h Correlation coefficient : = 0.886 Pressure on panel 1 when D is maximum :

  25. [ .(h) + (-h)] = qh2 h [ (-0.17)(0.20)(0.35)- (0.20)2 )] = qh [Cp2 + g p2,DCp2] = qh [(-0.60) + 4 (-0.602) (0.20)] = -1.08 qh Effective static loading distributions Effective pressures for maximum drag force : • Covariance between p2(t) and drag D(t) : = -(0.052) qh2 h Correlation coefficient : = -0.602 Pressure on panel 2 when D is maximum :

  26. +1.70 -1.08 Check : maximum drag force : = (1.70) qh (+h) + (-1.08) qh (-h) = 2.78 qh(h) (previously 2.79 qh(h) ) -1.08 +1.70 Effective static loading distributions Effective pressures for maximum drag force : Pressure coefficients corresponding to maximum drag :

  27. -0.73 -0.90 -0.90 -0.73 1 2 Effective static loading distributions Effective pressures for maximum lift force : Pressure coefficients corresponding to maximum uplift force:

  28. +1.65 -0.30 -0.30 +1.65 1 2 Effective static loading distributions Effective pressures for minimum lift force : Pressure coefficients corresponding to minimum uplift force: (maximum down force)

  29. fR (z) = gR m(z) (2 n1)2 1 (z) (=a) is the standard deviation of the modal coordinate Effective static loading distributions Resonant load distribution : gR is peak factor for resonant response m(z) is mass per unit length n1 is first mode natural frequency 1 (z) is the mode shape for the first mode of vibration where, x(z,t) = j aj (t) j (z) (modal analysis)

  30. Effective static loading distributions Combined load distribution : Wback and Wres are weighting factors Check : (correct expression)

  31. 45 - + C C =0.5 p R Extreme load distribution for the support reaction, R Extreme load distribution for the bending moment at C Gust pressure envelope Effective static loading distributions Example : Effective static load distributions for end reaction and bending moment on an arched roof (no resonant contribution):

  32. Effective static loading distributions Example : Effective static load distributions for base bending moment on a tower :

  33. End of Lecture 13John Holmes225-405-3789 JHolmes@lsu.edu

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