Internal pressures Wind loading and structural response Lecture 16 Dr. J.D. Holmes

Internal pressures Wind pressure on a wall cladding or roof is always : external wind pressure - internal pressure wind will affect internal pressure magnitude, except for fully sealed buildings Fully-sealed buildings : assume internal pressure is atmospheric pressure (p o ) Wind-induced internal pressures significant for dominant openings - e.g. produced by flying debris

Internal pressures Single opening on windward wall air flow into building  increase in density of air within the volume external pressure changes produced by wind - typically 1% of absolute air pressure internal pressure responds quickly to external flow and pressure changes Single Dominant Opening

Internal pressures Single opening on windward wall Dimensional analysis :  1 = A 3/2 /V o - where A is the area of the opening, and V o is the internal volume - where p o is atmospheric (static) pressure (related to Mach Number)  3 =  a  UA 1/2 /  - where  is the dynamic viscosity of air (Reynolds Number) (turbulence intensity)  5 = u /  A - where u is the length scale of turbulence

Internal pressures Single opening on windward wall Helmholtz resonator model : Air ‘slug’ moves in and out of building in response to external pressures Air ‘slug’ Mixing of moving air is ignored e

Internal pressures Single opening on windward wall Helmholtz resonator model : inertial term (mass times acceleration) for air slug damping - energy losses through opening stiffness - resistance of internal pressure to movement of slug A = area of opening, V o = internal volume  a = (external) air density, p o = (external) air pressure

Internal pressures Single opening on windward wall ‘Stiffness’ term : Assume adiabatic law for internal pressure and density Since  i   a, p i  p o Resisting force =  p i.A  = ratio of specific heats(1.4 for air)

Internal pressures Single opening on windward wall ‘Damping’ term : From steady flow through a sharp-edged orifice : k = discharge coefficient Theoretically k = Inertial term : Theoretically e =(circular opening)

Internal pressures Single opening on windward wall Converting to pressure coefficients : Second-order differential equation for C pi (t) Undamped natural frequency (Helmholtz frequency) : Increase internal volume V o : decrease resonant frequency, increase damping Increase opening area A : increase resonant frequency, decrease damping

Internal pressures Single opening on windward wall Helmholtz resonant frequency : Effect of building flexibility : K A = bulk modulus of air = pressure change for unit change in volume = (  a  p)/ , equal to  p o K B = bulk modulus for the building For low-rise buildings, K A / K B = 0.2 to 5 (for Texas Tech field building, K A / K B = 1.5)

Internal pressures Single opening on windward wall Helmholtz resonant frequency : (measured values for Texas Tech building) Resonant response is not high because of high damping

Internal pressures Single opening on windward wall Sudden windward opening (e.g. window failure) : Small opening area - high damping Large opening area - low damping - overshoot and oscillations V o = 600 m 3. A w = 1m 2. U = 30 m/s Time (secs ) Cp i V o = 600 m 3. A w = 9m 2. U = 30 m/s Time (secs) Cp i

Internal pressures Multiple openings on windward and leeward walls : Neglecting compressibility in this case (  a = 0) : Can be used for mean internal pressures or peak pressures using quasi-steady assumption. Need iterative solution when N is large. where (modulus allows for flow from interior to exterior) N is number of openings

Internal pressures Multiple openings on windward and leeward walls : Consider building with 5 openings : Q1Q1 Q2Q2 Q3Q3 Q4Q4 Q5Q5 p e,1 p e,2 p e,3 p e,4 p e,5 pipi inflows outflows

Internal pressures Single windward opening and single leeward opening : i.e. 2 openings : in terms of pressure coefficients, Equation 6.16 in book re-arranging,

Internal pressures Single windward opening and single leeward opening : i.e. comparison with experimental data : Used in codes and standards to predict peak pressures (quasi-steady principle) A W /A L  C pi Measurements Equation (6.16)

Internal pressures Multiple windward and leeward openings : Neglect inertial terms, characteristic response time : Characteristic frequency, n c = 1/(2  c ) A w = combined opening area on windward wall A L = combined opening area on leeward wall fluctuating internal pressures : numerical solutions required if inertial terms are included

Internal pressures Multiple windward and leeward openings : Effective standard deviation of velocity fluctuations filtered by building : High characteristic frequency - most turbulence fluctuations appear as internal pressures Low characteristic frequency - most turbulence fluctuations do not appear as internal pressures

Internal pressures Porous buildings : Treated in same way as multiple windward and leeward openings : A L = average wall porosity  total areas of leeward and side walls A w = average wall porosity  total windward wall area

End of Lecture 16 John Holmes