Calculating Influence Coefficients & Mean Components for Static & Background Loads, Slides of Environmental Law and Policy

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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)

Influence coefficient :

Value of a load effect as a unit load is moved around a structure :

Influence coefficient :

Value of a load effect as a unit load is moved around a structure :

Influence coefficient :

Value of a load effect as a unit load is moved around a structure :

Influence coefficient :

Value of a load effect as a unit load is moved around a structure :

Influence line - Central B.M.

-0.

0

0 0.2 0.4 0.6 0.8 1

position/total beam length

Influence coefficient :

Value of a load effect as a unit load is moved around a structure :

Influence line - Central B.M.

-0.

0

0 0.2 0.4 0.6 0.8 1

position/total beam length

Influence coefficient :

Value of a load effect as a unit load is moved around a structure :

Influence line - Central B.M.

-0.

0

0 0.2 0.4 0.6 0.8 1

position/total beam length

Influence coefficient :

Value of a load effect as a unit load is moved around a structure :

Influence line - Central B.M.

-0.

0

0 0.2 0.4 0.6 0.8 1

position/total beam length

Ir(z) z

For a distributed load p(z) , r =

L

0

p(z)Ir (z) dz

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Mean component

 p(z) = [0.5 aUh^2 ] Cp

on a tower :  f (z) = [0.5 a  U(z)^2 ] Cd

b(z) (per unit height)

Background (quasi-static) component

Consider a load effect r with influence line Ir(z):

Instantaneous value of r : r(t) = 

L

0

p(z,t) Ir (z) dz

p(z,t) = fluctuating pressure at z

L is length of the structure

Mean value of r : 

L

0

r p(z) Ir (z) dz

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)

L^1 /^2

0

1 2 r 1 r 2 1 2

L

0

σ (^) r,B p(z )p(z ) I (z ) I (z ) dzdz  

 (^)    

rˆ^ rgBσr,B

p r,B

L

0

1 r 1 1

pr σ (z) σ

p(z,t) p(z ,t) I (z ) dz

ρ (z)

  

 p r,B

1 r 1 1

L

0 σ (z) σ

p (z,t)p(z ,t)I (z ) dz





Background (quasi-static) component

Discrete form of pr :  (^) i k k  (^) pi r k

ρr, (^) pi p (t)p (t)I σ σ

This form is useful when using using wind-tunnel data obtained

from area-averaging over discrete measurement panels

k

I

i

(t)I

k

2 p (t)p

r

i k i

Standard deviation of load effect :  

Example (pitched free roof) :

(Appendix F in book)

2 1

22.5

h