2 ttl en 1991-1-1 densities (05-07-08)

Eurocode 1: Actions on Structures Part 1-1: General actions – Densities, self-weight, imposed loads for buildingsProfessor Haig Gulvanessian
EN 1991-1-1: Eurocode 1: Part 1-1: Densities, self-weight, imposed loads for buildings
Professor Haig Gulvanessian CBE
Associate BRE,
Professor Haig Gulvanessian
Scope of Presentation
EN 1991-1-1:2002 – Eurocode 1: Actions on Structures – Part 1-1: General actions – Densities, self-weight, imposed loads for buildings
Outline content
Compare with BS 6399 Parts 1 and 3 and BS 648
Outline UK National Annex to EN 1991-1-1
Identify topics covered in BS6399 but not in EN 1991-1-1 and vice versa
EN 1998
EN 1997
Actions on structures
Design and detailing
Section 3 Design Situations
Section 5 Self-weight Of Construction Works
Section 6 Imposed Loads On Buildings
Annex A (Informative) Tables For Nominal Density Of Construction Materials, And Nominal Density And Angles Of Repose For Stored Materials
Annex B (Informative) Vehicle Barriers And Parapets For Car Parks
Scope of EN 1991-1-1
Design guidance and actions for the structural design of buildings and civil engineering works, including:
- densities of construction materials and stored materials (Section 4 & Annex A),
- self-weight of construction elements (Section 5), and
imposed loads for buildings (Section 6),
BUT
Design of roofs - imposed loads due to occupancy and maintenance are given only in EN 1991-1-1 (unlike BS6399 Part 3). Snow Loads on roofs are given in BS EN 1991-1-3
Variation in time: Permanent, Variable or Accidental
Origin: Direct or Indirect
Nature and/or structural response: Static or Dynamic
Self-weight of construction works: generally a Permanent Fixed action, however
If Variable with time then represented by upper and lower characteristic values, and
If Free (e.g. moveable partitions) then treat as an additional imposed load.
Ballast and earth loads on roofs/terraces: Permanent with variations in properties (moisture content, depth) during the design life being taken into account.
Imposed loads on buildings: generally Variable Fixed or Variable Free actions
Mean (small variability)
EN 1991-1-1: Classification of Actions (cont)
Imposed loads generally quasi-static and allow for small dynamic effects in static structures. When dynamic response possible, a dynamic analysis is recommended as per the National Annex
Actions causing significant acceleration of structural members are classified as dynamic and need to be considered via a dynamic analysis
However for fork-lift trucks and helicopters additional inertial loads from hoisting and take-off/landing are accounted for through a dynamic magnification factor applied to appropriate static load values
EN 1991-1-1: Design Situations – Permanent Loads
The total self-weight of structural and non-structural members is taken as a single action when combinations of actions are being considered
Where it is intended to add or remove structural or non-structural members after construction critical load cases need to be identified and taken into account.
Water level is taken in to account for relevant design situations, as is the source and moisture content of materials in buildings used for storage purposes.
EN 1991-1-1: Design Situations – Imposed loads
Where areas are likely to be subject to different categories of loadings, the critical load case needs to be identified and considered
For roofs of buildings, imposed loads should not be considered to act simultaneously with snow loads or wind actions.
Characteristic values of densities of construction and stored materials should generally be used.
Where only mean values available, they should be taken as characteristic values in the design.
Mean values for a large number of different materials are given in EN 1991-1-1 Annex A.
For materials not in Annex A either:
- the characteristic value of density needs to be determined as per EN 1990, where a normal distribution may be assumed or,
- a reliable direct assessment carried out perhaps utilising EN 1990 Annex D.
Generally represented by a single characteristic value calculated from nominal dimensions, characteristic values of densities and including, where appropriate, ancillary elements, e.g. non-structural elements and fixed services, weight of earth and ballast.
As in BS6399 Part 1, loads due to moveable partitions are treated as imposed loads but in a slightly different way and there is no minimum load on floors of offices.
EN 1991-1-1: Treatment of movable partitions
Provided that a floor allows a lateral distribution of loads, the self-weight of movable partitions may be taken into account by a uniformly distributed load qk which should be added to the imposed loads of floors. This defined uniformly distributed load is dependent on the self-weight of the partitions as follows:
for movable partitions with a self-weight 1,0 kN/m wall length: qk =0,5 kN/m2;
for movable partitions with a self-weight 2,0 kN/m wall length: qk =0,8 kN/m2;
for movable partitions with a self-weight 3,0 kN/m wall length: qk =1,2 kN/m2.
EN 1991-1-1: Self-weight of construction works relating to highway bridges
A suite of clauses, specific to bridges, relating to depths of ballast/fill, thicknesses of surface coatings, weights of cables, pipes, service ducts and bridge furniture.
EN 1991-1-1: Self-weight of construction works relating to highway bridges (NA figures in yellow)
To determine the upper and lower characteristic values of self-weight of waterproofing, surfacing and other coatings for bridges, where the variability of their thickness may be high, a deviation of the total thickness from the nominal or other specified values should be taken into account. Unless otherwise specified, this deviation should be taken equal to ± 20 % (±40%) if a post-execution coating is included in the nominal value, and to + 40 % (+ 55 % ) and – 20 % (– 40 %) if such a coating is not included.
For the self-weight of cables, pipes and service ducts, the upper and lower characteristic values should be taken into account. Unless otherwise specified, a deviation from the mean value of the self-weight of ± 20 % (± 20 % ) should be taken into account.
For the self-weight of other non structural elements such as :
hand rails, safety barriers, parapets, kerbs and other bridge funiture,
joints/fasteners,
void formers,
the characteristic values should be taken equal to the nominal values unless otherwise specified.
EN 1991-1-1: Imposed loads on buildings
Characteristic values of loads for floors and roofs for the following types of occupancy and use:
residential, social, commercial and administration areas
garage and vehicle traffic
roofs
EN 1991-1-1: Imposed loads on buildings
Loads arise due to occupancy and the values given in EN 1991-1-1 account for
normal use by persons
furniture and moveable objects,
vehicles
rare events such as concentrations of people and furniture during times of re-organisation and refurbishment
Floor and roof areas in buildings are sub-divided into 11 categories according to use; loads specified are represented by uniformly distributed loads (UDL), concentrated loads, line loads or combinations thereof.
Heavy equipment such as may be found in communal kitchens or boiler rooms are specifically excluded from EN 1991-1-1. Need to be agreed with the Client and the relevant Authority for specific projects.
EN 1991-1-1:: Load values associated with various intensities of people loading
Main Categories of Use
- 4 categories (A, B, C and D)
Areas for storage and industrial activities
- 2 categories (E1 and E2)
Garages and vehicle traffic (excluding bridges)
- 2 categories (F and G)
Roofs
EN 1991-1-1: Imposed loads on buildings – Categories of use – residential, social, commercial and administrative
Imposed loads on buildings – Loads for floors, balconies and stairs for residential, social, commercial and administrative use
Clause NA 2.5 - Clause 6.3.1.2(10) (BSI National Annex)
Reduction factors for imposed loads – floors and accessible roofs
Equation NA 2.1 should be used instead of expression 6.1 recommended in EN 1991-1-1:2002 for evaluating the reduction factor aA,
aA = 1.0 – A/1000 ≥ 0.75 (NA 2.1)
where A is the area (m2) supported (see NOTE) .
NOTE: Loads that have been specifically determined from knowledge of the proposed use of the structure do not qualify for reduction.
Exp (6.1) - Clause 6.3.1.2(10)
EN 1991-1-1 Vs. NA
αA(BSI NA for EN 1991-1-1)
40
0,75
0,96
0,96
80
0,63
0,84
0,92
120
0,59
0,80
0,88
160
0,56
0,78
0,84
240
0,54
0,76
0,76
EN 1991-1-1 - Reduction factor αn for imposed loads from several storeys (Clause 6.3.1.2 (11))
Clause NA 2.6 - Clause 6.2.1.2 (11) (BSI National Annex)
‘Reduction factors for imposed loads from several storeys’
Equation NA 2.2 should be used instead of expression 6.2 recommended in EN 1991-1-1 for evaluating the reduction factor αn,
{1.1 - n/10 (1 ≤ n ≤ 5)
αn = {0.6 (5 < n ≤10) (NA 2.2)
{0.5 (n > 10)
where n is the number of storeys with loads qualifying for reduction (see NOTE).
Alternatively, load reductions based on area in NA 2.5 may be applied (i.e. if αA < αn.) However, the reductions given by equation NA 2.1 cannot be used in combination with those determined from equation NA 2.2.
NOTE: Loads that have been specifically determined from knowledge of the proposed use of the structure do not qualify for reduction.
Exp (6.2) Clause 6.2.1.2
EN 1991-1-1 - Reduction factor αn for imposed loads from several storeys. EN 1991-1-1 Vs NA
n
αn (BSI NA for EN 1991-1-1)
1
1
1
2
1
0,9
3
0,9
0,8
4
0,85
0,7
5
0,82
0,6
6
0,8
0,6
7
0,79
0,6
8
0,78
0,6
9
0,77
0,6
10
0,76
0,6
n
A
2
4
6
8
10
0.5
0.6
0.7
0.8
0.9
1
a
EN
n
EN 1991-1-1: Remarks on imposed load
Effect of actions that cannot exist simultaneously should not be considered together (EN 1990).
For local verification concentrated load Qk acting alone should be considered.
Reduction factors and n should not be considered together.
For the design of a column loaded from several storeys, load distributed uniformly.
For the design of a floor structure within one storey, the imposed load shall be considered at the most unfavourable part of the influence area.
Chess board arrangement Simplification in EN 1991-1-1
Mid span bending moment of a floor structure
Roofs
EN 1991-1-1: Imposed loads on buildings Categories and imposed loads on floors for storage and industrial use
EN 1991-1-1: Imposed loads on buildings: Fork lift and transport vehicles
Fork lifts and transport vehicles
Forklifts are classified into 6 classes via their hoisting capacity, which is reflected in other characteristics such as weight and plan dimensions.
For each class, a static axle load is defined which is then increased by a dynamic multiplication factor dependent on whether the forklift has solid (2,0) or pneumatic tyres (1,4). That factor is intended to account for the inertial effects caused by acceleration and deceleration of the hoisted load.
Where transport vehicles move on floors, either freely or guided by rails, the actions need to be determined from the pattern of the vehicle’s wheel loads. The static value of those wheel loads is determined from permanent weights and pay loads and the spectra of loads should be used to define appropriate combination factors and fatigue loads.
Roofs
EN 1991-1-1: Imposed loads on buildings Garage and traffic areas
Garage and vehicle traffic areas (excluding bridges)
Table 6.8 – Imposed loads on garages and vehicle traffic areas
Categories of traffic areas
qk [kN/m2]
Qk [kN]
Category F Gross vehicle weight: ≤ 30kN Category G 30kN < gross vehicle weight ≤ 160 kN
qk 5,0
Qk Qk
NOTE 1 For category F qk may be selected within the range 1,5 to 2,5 kN/m2 and Qk may be selected within the range 10 to 20 kN. NOTE 2 For category G, Qk may be selected within the range 40 to 90 kN NOTE 3 Where a range of values are given in Notes 1 & 2, the value may be set by the National annex. The recommended values are underlined.
Roofs
Roofs
Category H – Accessible for normal maintenance and repair only
Category I – Accessible with occupancy according to categories A to G
Category K – Accessible for special services e.g. helicopter landing areas
EN 1991-1-1: Imposed loads on buildings: Imposed loads on roofs
Table 6.10 – Imposed loads on roofs of category H
Roof
qk
Qk
NOTE 1 For category H qk may be selected within the range 0,0 to 1,0 kN/m2 and Qk may be selected within the range 0,9 to 1,5 kN. Where a range is given the values may be set by the National Annex. The recommended values are: qk = 0,4 kN/m2, Qk = 1,0kN NOTE 2 qk may be varied by the National Annex dependent upon the roof slope NOTE 3 qk may be assumed to act on an area A which may be set by the National Annex. The recommended value for A is 10m2, within the range of zero to the whole area of the roof. NOTE 4 See also 3.3.2 (1)
EN 1991-1-1: Imposed loads on buildings: Imposed loads on roofs - helicopters
Table 6.11 – Imposed loads on roofs of category K for helicopters
Class of Helicopter
Take-off load Qk
HC1 HC2
Qk = 20 kN Qk = 60 kN
0,2 x 0,2 0,3 x 0,3
Horizontal loads on parapets and partition walls acting as barriers
EN 1991-1-1: Annex A (informative) Tables for nominal density of construction materials, and nominal density and angles of repose for stored materials
Table A.1 - Construction materials-concrete and mortar
Table A.2 - Construction materials-masonry
Table A.3 - Construction materials-wood
Table A.4 - Construction materials-metals
Table A.6 - Bridge materials
Table A.8 - Stored products – agricultural
Table A.9 - Stored products - foodstuffs
Table A.10 - Stored products - liquids
Table A.11 - Stored products - solid fuels
Table A.12 - Stored products - industrial and general
EN 1991-1-1: ANNEX A: Table A.1 - Construction materials-concrete and mortar
Materials
Density [kN/m3]
concrete (see EN 206) lightweight density class LC 1,0 density class LC 1,2 density class LC 1,4 density class LC 1,6 density class LC 1,8 density class LC 2,0 normal weight heavy weight mortar cement mortar gypsum mortar lime-cement mortar lime mortar
9,0 to 10,0 1)2) 10,0 to 12,0 1)2) 12,0 to 14,0 1)2) 14,0 to 16,0 1)2) 16,0 to 18,0 1)2) 18,0 to 20,0 1)2) 24,01)2) >1)2) 19,0 to 23,0 12,0 to 18,0 18,0 to 20,0 12,0 to 18,0
1) Increase by 1kN/m3 for normal percentage of reinforcing and pre-stressing steel 2) Increase by 1kN/m3 for unhardened concrete
NOTE See Section 4
Materials
Density [kN/m3]
metals aluminium brass bronze copper iron, cast iron, wrought lead steel zinc
27,0 83,0 to 85,0 83,0 to 85,0 87,0 to 89,0 71,0 to 72,5 76,0 112,0 to 114,0 77,0 to 78,5 71,0 to 72,0
EN 1991-1-1: ANNEX A: Table A.12 - Stored products - industrial and general
Products
Angle of repose [°]
books and documents books and documents, densely stored filing racks and cabinets garments and rags, bundled ice, lumps leather, piled paper in rolls piled rubber rock salt salt sawdust dry, bagged dry, loose wet, loose tar, bitumen
6,0 8,5 6,0 11,0 8,5 10,0 15,0 11,0 10,0 to 17,0 22,0 12,0 3,0 2,5 5,0 14,0
- - - - - - - - - - 45 40 - 45 45 -
NOTE See Section 4.
EN 1991-1-1: Annex B - Vehicle barriers and parapets for car parks
Designated as an Informative Annex
Identical to Clause 11 of BS 6399 Part 1.
Impact force determined from:
- the velocity of the vehicle orthogonal to the barrier, and
- the deformations of both the vehicle and the barrier.
Values are given for two cases dependent upon gross mass of the vehicle, the dividing line being a vehicle of gross mass 2500kg.
Includes the forces that barriers on access ramps are required to resist.
The National Annex requires this Annex to be used in the UK
EN 1991-1-1: Annex B - Vehicle barriers and parapets for car parks
The horizontal characteristic force F (in kN), normal to and uniformly distributed over any length of 1,5 m of a barrier for a car park, required to withstand the impact of a vehicle is given by the expression below: (Clause B(2) of BS EN 199111:2002)
F = 0,5mv2 / (c + b)
m is the gross mass of the vehicle in (kg)
v is the velocity of the vehicle (in m/s) normal to the barrier
c is the deformations of the vehicle (in mm)
b is the deformations of the barrier (in mm)
Example
The graph below shows the variation of F for various deformations for
the vehicle and the barrier for a car of mass 1500kg.
Thus for b = 0 and c = 100, F = 150kN
Thus for b = 100 and c = 50, F = 100kN
0
100
200
0
100
200
Gives NDPs for 10 clauses
Many NDPs are to either:
- to confirm that the recommended values in the specified ranges are to be used, or if those values are not to be used,
- to select alternative values
Comment
Ranges generally permit the insertion of values from current practice i.e. insertion of appropriate values from BS 6399 Parts 1 and 3.
BS EN 1990 recommends partial factors for loads of
- self-weight 1,35 (c.f. UK 1,4), and
- imposed 1,5 (c.f. UK 1,6)
Thus direct insertion of UK values with EN 1990 factors will produce smaller ultimate limit state design loads.
Clause 2.2(3) ‘Dynamically Susceptible Structures’
The NA essentially gives the design guidance from BS6399 Part 1.
Clause 5.2.3 Additional Provisions Specific for Bridges
The NA gives values for the upper and lower characteristic values of the nominal depth and density of ballast taking into account consolidation (if appropriate), self-weight of surface coatings and cables, pipes and service ducts and other non-structural elements such as bridge furniture.
Clauses 6.3.1.1 Categories and 6.3.1.2 Values of Actions for residential, social, commercial and administrative areas
The NA sub-categories and gives corresponding load values for the categories in Table 6.1 of EN 1991-1-1. Sub-categories - essentially as Table 1 of BS6399 Part 1. Clause 6.3.1.2 gives methods for determining reduction factors for loaded areas of floors and imposed loads in columns from several storeys. The NA insists that the BS6399 Part 1 reduction factors should e used.
UK NA: Categories and Values of Actions for residential, social, commercial and administrative areas
UK National Annex for EN 1991-1-1: NDPs
Clauses 6.3.2.1 Categories and 6.3.2.2 Values of Actions for storage and industrial use
The NA gives the sub-categories and corresponding loads for category E1 (loads for storage) from Table 6.4 of EN 1991-1-1.
Clause 6.3.3.2 Values of Actions for garages and traffic areas
The NA replaces entries in Table 6.8 of EN 1991-1-1.
Clause 6.3.4.2 Values of Actions (imposed loads on roofs)
In the NA appropriate values replace the entries in Table 6.10 of EN 1991-1-1. The replacement values take account of the slope of the roof and are similar to the values for roofs accessible only for maintenance and repair given in BS6399 Part 3.
Clause 6.4 Horizontal loads on parapets and partition walls acting as barriers
In the NA, the entries in Table 6.12 of EN 1991-1-1 are replaced by those from Table 4 in BS6399 Part 1.
UK NA: Categories and Values of Actions for storage and industrial use
UK NA (via PD): Categories and Values of Actions for storage and industrial use Category E2
1 Imposed loads on garages and vehicle traffic area
2 Imposed loads on roofs (Category H)
1
2
UK NA: Categories and Values of Actions for minimum horizontal imposed loads for parapets, barriers and partition walls
Differences in scope between EN 1991-1-1 and BS 6399: Part 1
The scope of EN 1991-1-1 is more comprehensive than that of BS6399 Part 1. EN 1991-1-1 provides values for more types of imposed loads, and also covers imposed loads on roofs (covered by BS6399 Part 3), and the information given in BS 648.
Two areas which are in BS6399 but not in EN 1991-1-1:
- accidental loads on key or protected elements which are given in EN 1991-1-7, and
- vertical loads on parapets, barriers and balustrades.
Table 6.4 (BS)
Category of loaded
7.0
minimum of 6.5
9.0
minimum of 9.6
minimum of 15.0
minimum of 15.0
-
family or
a modular student accommodation unit with a secure door and comprising not more than
six single bedrooms and an internal corridor)
. Communal areas (including kitchens) in
b
locks of flats with limited use (See NOTE 1) (For communal areas in other blocks of
flats, see C3 and below)
A2
-
A3
A4
A5
: Balconies in single family dwelling units and communal areas in blocks of flats with
limited use (See NOTE 1)
A6
: Balconies in guest houses, residential clubs and communal areas in block
s of flats
A
cafes and restaurants (See NOTE 2)
C11
C12
C21
-
institutional type buildings (pedestrian traffic only, i.e. not subject to crowds or
wheeled
vehicles), hostels, guest houses, residential clubs, and communal areas in blocks of flats
not covered by NOTE 1. (For communal areas in flats covered by NOTE 1, see A)
C31
-
nstitutional
type buildings (pedestrian traffic only, i.e. not subject to crowds or wheeled vehicles),
hostels, guest houses, residential clubs, and communal areas in blocks of flats not
covered by NOTE 1. (For communal areas in flats covered by NOTE 1, se
e A)
-
all other buildings including hotels and motels and institutional buildings (pedestrian
traffic only).
-
all other buildings including hotels and motels and institutional buildings subject to
wheeled vehicles, trolleys etc.
-
buildings includin
g hotels and motels and institutional buildings (pedestrian traffic only)
C35
-
C36
-
C38
-
exhibition purposes
-
stages (See NOTE 5)
-
-
halls, bars, places of worship (See NOTES 4 and 5)
C
-
D
Shopp
ing
Areas
D1/D2
: Shop floors for the sale and display of merchandise.
NOTE 1. Communal areas in blocks of flats with limited use refers to blocks of flats not more than three storeys in
height and with not more than four self
-
floor accessible from one staircase.
-
.
Reference should also be made to NOTE 5.
NOTE 3. Fixed seating is seating where its removal and the use of the space for other purposes is improbable.
NOTE 4. For grandstands and stadia, see the requirements of the appropriate certifying authority.
NO
TE 5. For structures that may be susceptible to resonance effects reference should be made to Section NA 2.1 of
this National Annex
b
b
B
D
1)
rooms, receptions
lecture halls,
C3
, e.g. areas in
administ
C4
,
events like concert halls, sports h
alls including stands, terraces and
access areas and railway platforms.
D
Shopping
a
reas
D1
D2
1)
Attention is drawn to 6.3.1.1(2), in particular for C4 and C5. See EN 1990 when dynamic effec
ts need to be
NOTE 1.
Depending on their anticipated uses, areas likely to be categorised as C2, C3, C4 may be
categorised as C5 by decision of the client and/or National annex.
NOTE 2.
The National annex may p
rovide sub categories to A, B, C1 to C5, D1 and D2
NOTE 3.
Table 6.2(BS)
Categories of Loaded
access but with a minimum of 3.0
2.0
-
access but with a minimum of 4.0
2.0
b
b
B
D
1)
rooms, receptions
lecture halls,
C3
, e.g. areas in
administ
C4
,
events like concert halls, sports h
alls including stands, terraces and
access areas and railway platforms.
D
Shopping
a
reas
D1
D2
1)
Attention is drawn to 6.3.1.1(2), in particular for C4 and C5. See EN 1990 when dynamic effec
ts need to be
NOTE 1.
Depending on their anticipated uses, areas likely to be categorised as C2, C3, C4 may be
categorised as C5 by decision of the client and/or National annex.
NOTE 2.
The National annex may p
rovide sub categories to A, B, C1 to C5, D1 and D2
NOTE 3.
s
G
1,65
s
G
1.65
s
G
G
k,inf
G
k,sup
m
G
s
G
Category
(institutional and public buildings)
E12
E13
ffices)
E14
E16
and institutional buildings
w
arehouses
E1
Categories of traffic areas
NOTE: q
a
y
A
A
A
A
m
Loaded areas
Category C5
Category E
Category F
Category G
k
0,5
NOTE 2 For categories C2 to C4 and D q
k
-
3,0
k
2,0
kN/m. For areas of
category E the horizontal loads depend on the occupancy. Therefore the value of q
k
minimum value and should be checked for the specific occupancy.
NOTE 5 Where a range of values is given in Notes 1, 2, 3 and 4, the value may be set by the National
Annex. The recommended value is underlined.
NOTE 6 The National Annex m
ay prescribe additional point loads Q
k
Table 6.2
Categories of loaded areas
7,0
NOTE: Where a range is given in this table, the value may be set by the National annex. The
recommended values, intended for separate application, are underline
d. q
k
conditions of use of this Table.
Table 6.3
Category
documents
E2
Categories of loaded areas
usage (see Table 6.3 and Annex A)
for the particular project or by the National annex.
q
k
and Q
ferent conditions of use of
Table
6.4.
2
n
n
Roof Slope (Degrees)
partition walls
Loaded Areas
Examples (sub
dwelling including stairs, landings etc but
excluding external balconies and ed
ges of
office and institutional buildings
within 530mm
1.0
0.8
Footways within building curtilage and
adjacent to basement/sunken areas.
For areas where overcrowding may occur,
see C5
sunken areas
auditoria, shop
adjacent to sunken areas
as give
n below
industrial and storage buildings except
designated escape routes
more than 600mm wide
s
floors, footways , edges of roofs
1.5
1991
Category
Table NA.3
used in theatres to hang scenery,
curtains, etc.)
basaltic ballast
timber sleepers with track fastenings
1,2
4,8
bridge beam and guard rails
1,7
4,9
1)
2)
3)
Assumes a spaci
ng of 600mm
NOTE 1 The values for track are also applicable outside railway bridges.
NOTE 2 See Section 4.

2 ttl en 1991-1-1 densities (05-07-08)

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