Design for walking excitation DG11

Tekla Structural Designer
2021
Tekla Structural Designer

Design for walking excitation DG11

Floor slab

Slab Properties

For composite slabs the transformed moment of inertia per unit width of the slab, Ds, is calculated from,

Ds
 = 
de3 /(12*n)
  
mm4/mm in metric units
Ds
 = 
12*de3/(12*n)
  
ins4/ft in US Customary units
Where
de
  =  
effective depth of slab taken as slab depth less one half depth of steel decking (mm or inches)
n
  =  
dynamic modular ratio
  =  
Es /(1.35*Ec )
Es
  =  
the steel modulus (N/mm2 or ksi)
Ec
  =  
the concrete modulus (N/mm2 or ksi)

For generic slabs, the transformed moment of inertia per unit width is to be provided by the user.

Beam panel mode

Beam Panel Mode Deflection

The beam panel mode deflection, Δj, is the maximum simply supported deflection of the beam or joist calculated using,

Δj
  =  
5 * ((w*b)+wswt ) * Lj4 /(384*Es *Isj)
where
w
  =  
unit supported weight (psi or N/mm2 )
b
  =  
beam or joist spacing (in or mm)
wswt
  =  
beam or joist self weight (zero unless self weight loadcase in combination) (pli or N/mm)
Lj
  =  
span of beam or joist (in or mm)
Es
  =  
steel modulus (psi or N/mm2 )
Isj
  =  
the inertia of the beam or joist from the database (in4 or mm4)

Beam Panel Mode Frequency

The beam panel mode fundamental frequency, fj, is given by,

fj
  =  
0.18*√(g/Δj) Hz
Where
g
  =  
the acceleration of gravity
Δj
  =  
the maximum simply supported deflection of the beam or joist calculated as above.

Beam Panel Mode Effective Weight

The effective panel weight for the beam panel mode, Wj, is given by,

Wj
  =  
kj *w*Bj *Lj
Where
kj
  =  
beam continuity factor
  =  
1.0 generally but 1.5 where beams are continuous over supports and an adjacent span is > 0.7*Lj
w
  =  
unit supported weight (see Data Derived from Tekla Structural Designer)
Bj
  =  
the effective width of the beam panel
  =  
Cj *(Ds /Dj )0.25 *Lj but ≤ (2/3)*FW
Lj
  =  
the span of the beam
and
Cj
  =  
effective width coefficient for beam
  =  
2.0 generally but 1.0 for beams parallel to interior edge
Ds
  =  
transformed moment of inertia of slab per unit width as above
Dj
  =  
transformed moment of inertia of beam per unit width
  =  
Ij /S
S
  =  
beam spacing
FW
  =  
floor width
  =  
ng *Lg
ng
  =  
number of bays in the direction of the girder span.
Lg
  =  
the span of the girder

Girder panel mode

Girder Panel Mode Deflection

The girder panel mode deflection, Δg, is the maximum girder deflection derived from the analysis model.

Note: As Δg is taken directly from load analysis there is no need for any adjustment to the girder deflection, as suggested in DG11 section 3.1, when there is only one supported beam.

Girder Panel Mode Frequency

The girder panel mode fundamental frequency, fg, is given by,

fg
  =  
0.18*√(g/Δg) Hz
Where
g
  =  
the acceleration of gravity
Δg
  =  
the maximum simply supported deflection of the girder derived from the analysis model.

Girder Panel Mode Effective Weight

The effective panel weight for the girder panel mode, Wg, is given by,

Wg
  =  
kg * w *Bg * Lg
Where
kg
  =  
girder continuity factor
  =  
1.0 generally but 1.5 where girders are continuous over supports and an adjacent span is > 0.7*Lg
w
  =  
unit supported weight (see Data Derived from Tekla Structural Designer)
Bg
  =  
the effective width of the girder panel

For the general case,

Bg
  =  
Cg *(Dj /Dg)0.25 *Lg but ≤ (2/3)*FL

If the girder is an interior edge girder as specified by the user,

Bg
  =  
Lj*(2/3)
Where
Lg
  =  
the span of the girder
Cg
  =  
effective width coefficient for beam
  =  
1.8 generally but 1.6 for girders supporting joists connected to the girder flange (joist seats)
Dj
  =  
transformed moment of inertia of beam per unit width as above
Dg
  =  
transformed moment of inertia of girder per unit width
  =  
Ig/Lj generally but
  =  
2*( Ig/Lj) for edge girders
FL
  =  
floor length
  =  
nj *L j
nj
  =  
number of bays in the direction of the beam span.

If the girder supports beams with unequal spans, say Lj1 and Lj2, the average beam span length Lav = (Lj1+Lj2)/2 should replace Lj in the above equation for Dg. The user should confirm the value to be used in such circumstances.

Combined panel mode

There are three possible conditions is to be checked for the combined mode.

If Lg/Bj > 1.0, the combined equivalent panel weight, Wcomb, is given by,

Wcomb
  =  
j/(Δjg))*Wj + (Δg/(Δjg))*Wg
The floor fundamental frequency, fcomb, is given by
fcomb
  =  
0.18*√g/(Δjg)
If 0.5 ≤ Lg/Bj ≤ 1.0, the combined equivalent panel weight, Wcomb, is given by,
Wcomb
  =  
j/(Δjgred))*Wj + (Δgred /(Δj+ Δgred))*Wg
The floor fundamental frequency, fcomb, is given by
fcomb
  =  
0.18*√g/(Δj+ Δgred)
Where
Δgred
  =  
(Lg/Bj)* Δg

If Lg/Bj < 0.5, the combined equivalent panel weight, Wcomb, is given by,

Wcomb
  =  
j/(Δjgred))*Wj + (Δgred /(Δj+ Δgred))*Wg
The floor fundamental frequency, fcomb, is given by
fcomb
  =  
0.18*√g/(Δj+ Δgred)
Where
Δgred
  =  
0.5* Δg

In addition, if Lj/Lg < 0.5, then the peak acceleration ratio is separately checked for the beam panel mode and for the combined panel mode as above.

Evaluation

The peak acceleration ratio, ap/g, is evaluated for each fn in turn (with its associated W), and is given by,

ap/g
  =  
MAX[100*P0*e(-0.35*fn)/(β*W)] %

where

fn
  =  
fj, fg, fcomb
W
  =  
the value of Wj, Wg or Wcomb appropriate to fn
P0
  =  
constant force equal to 0.290 kN [65lb]
β
  =  
damping ratio

The acceleration limit, ao/g, is a user input and leads to the final design condition,

ap/g
ao/g
Note: The ‘fundamental frequency of the floor’ output in the results is the fn associated with the MAX peak acceleration ratio (and not just the MIN fn).

High Frequency Floors

For floor systems having a natural frequency greater than 9 Hz (but ≤ 15 Hz ), the equivalent sinusoidal peak acceleration ratio, aESPA/g, is given by

aESPA/g
  =  
MAX[100*(154 /W)*(fstep1.43/fn0.3)*{[1-e(-4*π*h*β)]/(h*π*β)}0.5] % US-units
  =  
MAX[100*(686 /W)*(fstep1.43/fn0.3)*{[1-e(-4*π*h*β)]/(h*π*β)}0.5] % metric-units

where

W
  =  
the value of Wj, Wg or Wcomb appropriate to fn
fstep
  =  
footstep frequency Hz
fn
  =  
fundamental frequency of the floor
h
  =  
the harmonic matching fn
  =  

5 for 9 Hz < fn ≤ 11 Hz

  =  

6 for 11 Hz < fn ≤ 13.2 Hz

  =  

7 for 13.2 Hz < fn ≤ 15 Hz

β
  =  
damping ratio
Note: The aESPA/g equation assumes a bodyweight value of 168 lbs [0.75 kN] as indicated in DG11.

The acceleration limit for high frequency floors is a user input and leads to the final design condition,

aESPA/g
acceleration limit for high frequency floors
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