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Imperfections of slender glulam beams

Authors:
Imperfections of slender glulam beams
Prof. Dr.-Ing. Ulrike Kuhlmann, Head of Institute
Janusch Töpler, M.Sc., Scientific Researcher
Institute of Structural Design, University of Stuttgart
Keywords: Imperfections, lateral torsional buckling, glulam beams, on-site measure-
ments, assembly tolerances, numerical modelling
1 Introduction
Imperfection assumptions are essential for the design verification of imperfection-sen-
sitive (slender) timber members and adjacent structural elements, including roof brac-
ings and fork bearings (LARSEN (1977)), (KUHLMANN & HOFMANN (2016)). However only
few imperfection measurements concerning timber buildings exist (BRÜNINGHOFF
(1973)), (DIETSCH & HENKE (2010)), (EHLBECK & BLAß (1987)), (KESSEL & KÜHL & HALL (2015)),
yet there is a lack of sufficient data regarding slender roof girders. Furthermore, the
equivalent imperfections in EN 1995-1-1 (2004), on which the verifications of in-plane
buckling and lateral torsional buckling are based, are inconsistent (e.g. initial bow im-
perfections for glulam included in the effective length method in-plane buckling (kc-
method): ey L/1100 and lateral torsional buckling (kcrit-method): ey ≈ L/288 to L/577)
(EHLBECK & BLAß (1987)), (HEIMES-
HOFF (1986)). Consequently, due to
the possibility of conservative as-
sumptions of imperfections, load-
bearing capacity reserves may be
expected in the verification of tim-
ber members at risk of lateral tor-
sional buckling, when using the ef-
fective length method or design
verification according to second
order theory. Also, in achieving a
more economical design of fork
bearings, there is a lack of know-
Figure 1.1. On-site imperfection measurement with a laser
scanner Leica ScanStation P20 (building 2020-KW34).
ledge referring to the assembly tolerances of long-spanning roof structures (KUHLMANN
& HOFMANN (2013)).
Within a DIBt research project (KUHLMANN & TÖPLER (2021 b)), measurements of the as-
sembly tolerances of timber building structures were carried out by the Institute of
Structural Design from 2020 to 2021 (Figure 1.1), in order to create a database of ge-
ometric imperfections of slender glulam beams and to develop consistent proposals
for equivalent imperfections. These should contribute to the current revision of
EN 1995-1-1 (2004) and the preparation of the new European standard “Execution of
Timber Structures”.
This paper presents the results of imperfection measurements on 139 slender glulam
beams in 13 timber buildings using a laser scanner (Figure 1.1) conducted in 2020. Us-
ing numerical methods, equivalent imperfections and torsional moments at the fork
bearings are determined. The results are compared with current design rules.
2 Imperfection measurements
2.1 General
As part of the DIBt research project DIBt - ZP 52-5-13.194, assembly tolerances of ap-
proximately 25 timber buildings shortly after assembly have been determined with a
laser scanner from 2020 to 2021. Buildings with glulam beams made of softwood and
beam-columns made of beech LVL were surveyed. The measurements were carried
out in cooperation with the Institute for Photogrammetry at the University of Stuttgart.
This paper reports on the measurement results of the glulam beams.
Detailed explanations can be found in the interim report of the research project
(KUHLMANN & TÖPLER (2021 b)).
2.2 Measurement programme, setup and execution
2.2.1 Measurement programme
Table 2.1 lists the 13 buildings with 139 slender glulam beams reported. To ensure the
representativeness of the sample of timber buildings, typical beam geometries (span L,
cross-sectional dimensions H and W and beam shape) and material grades commonly
used in construction practice in the DACH (Germany, Austria, Switzerland) region were
covered. The timber buildings’ elements were fabricated und erected by different
manufacturers and assembly companies.
All buildings were single-storey industrial halls with roof constructions made of slender
glulam beams (see e.g. Figure 1.1). The beam span of the evaluated members ranged
between 6.9 m and 42.4 m, cross-sectional height between 0.69 m and 2.68 m and
cross-sectional width between 0.14 m and 0.26 m. Material grades of the beams were
GL 24h and GL 28c and roof bracings were realised by means of steel/timber diagonals,
glulam roof panels or fixed columns.
Table 2.1. Measured buildings with slender glulam beams.
Building
Beam
shape
Span
[m]
Cross-sectional
height/width
Material
Bracing system
2020-KW23
14.5
5.1
GL 28c
Steel diagonals
2020-KW27
29.6
12.2
GL 24h
Timber diagonals
2020-KW32
23.6
9.0
GL 28c
Timber diagonals
2020-KW33
17.9
8.8
GL 28c
Steel diagonals
2020-KW34
13.1 -
17.5
6.5 - 12.6
GL 24h
Timber diagonals
+ fixed columns
2020-KW38_1.1
17.4
5.0
GL 28c
Glulam roof
panel
2020-KW38_1.2
9.9
3.6
GL 24h
Glulam roof
panel
2020-KW38_1.3
10.0
3.8
GL 24h
Glulam roof
panel
2020-KW38_1.4
6.9
2.9 + 4.8
GL 24h
Glulam roof
panel
2020-KW38_2
42.4
10.6
GL 28c
Timber diagonals
2020-KW45_1.1
23.5
9.2
GL 28c
Steel diagonals
2020-KW45_1.2
26.5
9.3
GL 28c
Steel diagonals
2020-KW47
20.8
6.8
GL 24h
Timber diagonals
The measurements were taken directly after assembly and alignment of the timber
structures. In some cases, the structures were loaded by roofing and wall cladding in
addition to their self-weight. The influence of wind actions during the measurement
can be neglected, as the estimated Beaufort number describing the wind speed was
always ≤ 5 (fresh breeze).
The measured geometry of the structures thus particularly includes influences from
assembly, transport and production. Influences from the loading, the long-term behav-
iour and slip within the connections, which might occur at the first significant loading
of the roof structures, are not included in the measurement results (or only included
to a negligible extent).
2.2.2 Measurement setup and execution
The measurements were carried out with a Leica ScanStation P20 laser scanner (Figure
1.1), which records measurement points in a grid of 3.1 mm x 3.1 mm when assuming
a distance of 10 m (Leica Geosystems AG (2013)). Using several measurement loca-
tions per building, a 3D point cloud of the entire structure was generated from the
ground surface (Figure 2.1). The total measurement time per building was between 1.5
and 5 hours.
In addition, the air temperature and humidity and, if possible, the wood moisture con-
tent were determined in at least three structural elements per building with a Trotec
T2000 multifunctional measuring device. Furthermore, information was collected con-
cerning the building structure, material, manufacture, transport, assembly process,
weathering, surface quality and any damage to the timber members.
2.3 Measurement results
2.3.1 Evaluation
The measurement error of a measurement point at a distance of the laser scanner to
the object of approx. 15 m is specified in the laser scanner manual as approx. 1 mm in
the x, y and z directions (position accuracy and range noise) (LEICA GEOSYSTEMS AG
(2013)). This coincides with observed deviations when evaluating the measurement
results of individual point coordinates. Therefore, in the evaluation, average values of
the point coordinates of 200 to 1000 measuring points were always calculated,
whereby the accuracy of the averaged point coordinates could be increased to less
than 0.1 mm (at a confidence level of 90 % according to (FISCHER (2003)) in the x, y and
z directions. Since this is a random error, with expected horizontal bow imperfections
ey of the beams of approx. L/1000 = 6.9 mm (Table 2.1, min L = 6.9 m), the measuring
accuracy of the laser scanner is sufficient.
The point clouds (Figure 2.1) were automatically evaluated using Matlab software. The
coordinate system used is shown in Figure 2.2. The results of the evaluation are the y
and z coordinates of the beam axis over the beam length (bow imperfections ey) and
the torsion of the cross-section around the x-axis (twist imperfections eϑ). Figure 2.3
shows examples of measured horizontal bow imperfections ey and Figure 2.5 displays
the twist imperfections eϑ over the beam length (x direction). eϑ describes the twist of
a cross-section around the x-axis without units (gradient of a straight line to the verti-
cal).
Figure 2.1. Point cloud from laser scan measurements
(building 2020-KW34), the colour represents the intensity of
the laser signal and has no further meaning.
Figure 2.2. Generally used coordinate
system.
x
y
z
2.3.2 Results
Figure 2.3 shows typical curves of the measured horizontal bow imperfections ey of the
beam axis over the beam length (x direction). The ideal planned beam position with
the two supports “ x is shown as a dash line - - ”. Essential observations when as-
sessing the bow imperfection curves are:
The shape of the bow imperfection over the beam length usually (122 of 139 beams)
corresponded approximately to a sinusoidal or parabolic curve (Figure 2.3 (b) and
(d)). In some cases (11 of 139 beams) a bump shape occurred (Figure 2.3 (a)). How-
ever, in a few cases (6 of 139 beams) a change in the sign of the bow imperfections
ey was observed at a point of application of a compression purlin (Figure 2.3 (c)). In
general, the bow imperfection curves could be represented by a sinusoidal half-
wave (Kuhlmann & Töpler (2021 b)).
Over the beam length, discontinuity points / outliers of individual y coordinates were
sometimes observed, which were attributed to local defects (e.g. knotholes) or con-
nected members such as purlins. These were neglected in the evaluation.
Figure 2.4 shows the maximum values of the measured horizontal bow imperfections
ey of 139 glulam beams, separated by buildings (see also Table 2.1). Additionally the
results of measurements on 7 beams of (DIETSCH & HENKE (2010)) are added in the dia-
gram. The x-axis displays the beam span (distance between the supports of the struc-
tural system) and the y-axis exhibits the bow imperfections ey. Each data point repre-
sents the maximum measured horizontal bow imperfection (not necessarily at mid-
span, Figure 2.3) of a beam. In addition, the equivalent bow imperfection for calcula-
tions according to second order theory (EN 1995-1-1 (2004)) with L/400, and the value
(a) Building 2020-KW32 - Beam axis 7
(b) Building 2020-KW33 - Beam axis 4
(c) Building 2020-KW38_2 - Beam axis 25
(d) Building 2020-KW45_1.1 - Beam axis 8.2
Figure 2.3. Typical curves of the measured horizontal bow imperfections ey, or elevated top view of
the beams, with x-axis as longitudinal axis.
-0.02
-0.01
0.00
0.01
0.02
0.0 4.0 8.0 12.0 16.0 20.0 24.0
ey[m]
x [m]
Beam axis 7
-0.010
-0.005
0.000
0.005
0.010
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0
ey[m]
x [m]
Beam axis 4
-0.010
-0.005
0.000
0.005
0.010
0 4 8 12 16 20 24 28 32 36 40 44
ey[m]
x [m]
Beam axis 25
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.0 4.0 8.0 12.0 16.0 20.0 24.0
ey[m]
x [m]
Beam axis 8.2
L/1000 are displayed. All measured bow imperfections ey were below L/400. A maxi-
mum bow imperfection ey of L/1000 was exceeded by 18 of the 139 glulam beams
(13 %). For buildings with beams with measured ey > L/1000, assembly difficulties were
reported due to small tolerances of connectors (2020-KW27), one of two roof bracings
was not aligned according to generally accepted standards (2020-KW45_1.1), or the
beams were braced by glulam roof panels and therefore could not be aligned horizon-
tally during assembly (2020-KW38_1.1). When looking at the scatter band, the linear
relationship between bow imperfection ey and beam span assumed in EN 1995-1-1
(2004) is generally confirmed. A significant influence of the horizontal beam stiffness
on the measured bow imperfections ey could not be found.
The measurement results (DIETSCH & HENKE (2010)) are somewhat less favourable (Fig-
ure 2.4), which could be due to the fact that the 7 measured beams were not only
loaded by their self-weight and were partly already subjected to long-term influences.
Figure 2.5 shows typical curves of the measured twist imperfections eϑ around the x-
axis over the beam length (x direction). A positive twist eϑ means that the measured y
coordinate of the upper edge of the beam is greater than that of the lower edge of the
beam (see Figure 2.6). The ideal planned beam position with the two supports “ x “ is
shown as a dash line “ - - ”. Essential observations when assessing the twist imperfec-
tion curves are:
Unlike the bow imperfection curves, the shape of the twist imperfections over the
beam length cannot be assigned to a generally valid curve shape.
The maximum twist imperfection often occurred at supports (104 of 139 beams),
Figure 2.4. Maximum measured horizontal bow imperfections of 139 glulam beams with scatter band
(blue) plotted for 87 % of the measured values, measurement results of 7 beams of (DIETSCH & HENKE
(2010)) added, span shown on the x-axis and bow imperfections on the y-axis, each data point
representing one beam.
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0
Bow imperfection ey[mm]
Span [m]
L/1000
L/400
2020-KW23
2020-KW27
2020-KW32
2020-KW33
2020-KW34
2020-KW38_1.1
2020-KW38_1.2
2020-KW38_1.3
2020-KW38_1.4
2020-KW38_2
2020-KW45_1.1
2020-KW45_1.2
2020-KW47
Dietsch & Henke (2010)
especially if the fork bearings were designed as a reinforced concrete pockets.
The shape of the twist imperfections along the beam length was in some cases (23
of 139 beams) approximately sinusoidal or parabolic (Figure 2.5 (a)). But in general,
the maximum eϑ was either at one support (43 beams, Figure 2.5 (b)), at both sup-
ports with the same sign (44 beams, Figure 2.5 (c)), or at both supports with oppo-
site signs (17 beams, Figure 2.5 (d)). Not all of the beams could clearly be assigned
to one of these cases.
Figure 2.6 shows the maximum values of eϑ x H (differences of the measured horizontal
displacements of the top edge to the bottom edge of the beam) of the 139 glulam
beams, separated by buildings (see also Table 2.1). Additionally the results of meas-
urements on 6 beams of (DIETSCH & HENKE (2010)) are added in the diagram. The x-axis
displays the beam span (distance between the supports of the structural system) and
the y-axis exhibits eϑ x H (twist imperfection x beam height). Each data point represents
the absolute maximum value (not necessarily at midspan, Figure 2.5) of a beam. The
measured values show increasing horizontal differential deformations eϑ x H between
the top and bottom edge of the beam as the span increases. This relationship is also
shown by the regression line eϑ x H = 0.0005 x L, which results from the evaluation of
the data. The measurement results (DIETSCH & HENKE (2010)) fit well into the overall pic-
ture of the own measurement results.
The correlation eϑ = 0.05 x Width / Height found by (LARSEN (1977)) on solid wood test
specimens cannot be confirmed by the measurement results.
In Figure 2.6 measured values of beams with fork bearings not made of reinforced con-
crete pockets (e.g. fork bearing by means of lateral timber plates), are marked in blue.
(a) Building 2020-KW23 - Beam axis 2
(b) Building 2020-KW32 - Beam axis 5
(c) Building 2020-KW33 - Beam axis 3
(d) Building 2020-KW45_1.2 - Beam axis 5.3
Figure 2.5. Typical curves of the measured twist imperfections eϑ around the x-axis, with x-axis as
longitudinal axis.
-0.015
-0.010
-0.005
0.000
0.005
0.0 3.0 6.0 9.0 12.0 15.0
eϑ[-]
x [m]
Beam axis 2
-0.025
-0.020
-0.015
-0.010
-0.005
0.000
0.005
0.0 4.0 8.0 12.0 16.0 20.0 24.0
eϑ[-]
x [m]
Beam axis 5
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0
eϑ[-]
x [m]
Beam axis 3
-0.025
-0.020
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
0.0 4.0 8.0 12.0 16.0 20.0 24.0 28.0
eϑ[-]
x [m]
Beam axis 5.3
Such a design seems to favour smaller assembly tolerances with regard to the twist
imperfections.
3 Numerical simulations
3.1 General
The numerical calculations were executed with a FE-model in Abaqus/CAE 2018. The
aim being to investigate the stability behaviour of the measured beams and to deter-
mine equivalent imperfections, as well as to examine the torsional moments at the
supports. For each measured beam, calculations of eigenvalues (model 1), computa-
tions with measured imperfections (model 2) and with equivalent imperfections
(model 3) have been carried out.
3.2 Numerical modelling and calculation procedure
In Figure 3.1 the numerical model of the building 2020-KW23 is displayed. The beam
was modelled according to the ideal planned geometry. The horizontal stabilising in-
fluence of the roof bracing was taken into account by an equivalent beam, where the
stiffness was determined based on (KESSEL & SIEDER & KREUZINGER (2020)). The stiffness
of the purlins was mapped by equivalent springs acting only in y direction. For the glu-
lam beam, 20-node quadratic brick elements with a mesh fineness of 100 elements in
length, 10 elements in height and 8 elements in width were chosen. An orthotropic
material model with mean material properties according to EN 14080 (2013), Poisson’s
ratios according to (NEUHAUS (1981)), bilinear elasto-plastic material behaviour under
compression along the grain and linear elastic material behaviour under tension along
Figure 2.6. Maximum measured twist imperfections around the x-axis of 139 glulam beams,
measurement results of 6 beams of (DIETSCH & HENKE (2010)) added, span shown on the x-axis and
eϑ x H on the y-axis, each data point representing one beam, blue marked are measured values of
beams with fork bearings not made of reinforced concrete pockets.
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0
eϑx H [mm]
Span [m]
2020-KW23
2020-KW27
2020-KW32
2020-KW33
2020-KW34
2020-KW38_1.1
2020-KW38_1.2
2020-KW38_1.3
2020-KW38_1.4
2020-KW38_2
2020-KW45_1.1
2020-KW45_1.2
2020-KW47
Dietsch & Henke (2010)
regression line
0.0005 x L
Twist imperfection:
eϑ
eϑx H
y
z
-1 -
the grain was used. The grain direction was chosen parallel to the bottom edge of the
beam, also for curved beams. The load was applied by means of a line load at the upper
edge of the beam. The calculations on model 2 and 3 were performed as geometrically
and materially non-linear analysis with imperfections (GMNIA, prEN 1993-1-14 (2021)).
The verification of the numerical models was achieved according to prEN 1993-1-14
(2021) (see also (KUHLMANN & TÖPLER (2021 a)).
In model 1 no imperfections and purely elastic behaviour were considered. Using
model 1, the eigenvalues and eigenmodes of a beam were determined and the relative
slenderness ratio λrel,m and resulting lef,m were evaluated (EN 1995-1-1 (2004)).
In model 2 the measured imperfections were assumed. By means of model 2, the max-
imum load-bearing capacity and associated line load qmax of a beam, at which the ten-
sile stress σx reaches the characteristic bending strength fm,k (EN 14080 (2013)), was
computed.
In model 3 the equivalent imperfections were applied. Due to the possible
eigenmodes, both global equivalent imperfections (wavelength / 2 = beam span), local
equivalent imperfections (wavelength / 2 = distance between purlins) and a superpo-
sition of both imperfections were included in preliminary investigations (Figure 3.2).
While model 2 obtained the line load qmax which was then applied in model 3. The
corresponding bending stresses and the ratio σx / fm,k (= utilization μx), which indicates
Figure 3.1. Numerical model of the double-tapered beams in building 2020-KW23.
Figure 3.2. Bow imperfections for the numerical modelling, beam axis 2 in building 2020-KW23.
Measured beam
Equivalent beam - bracing
Equivalent spring - purlins
Equivalent spring - eaves purlin
-0.010
-0.005
0.000
0.005
0.010
0.015
0.0 3.0 6.0 9.0 12.0 15.0
ey[m]
x [m]
measured imperfection
global imperfection
local imperfection
global + local imperfection
Application points - purlins
to what extend the approach of the equivalent imperfections is suitable to represent
the real beam behaviour (with measured imperfections), were determined.
This procedure was carried out for all 139 beams. Additionally the torsional moments
at the supports Mx were derived for all of the beams based on model 2 and 3.
3.3 Results and evaluation
3.3.1 General
The horizontal stiffness of the roof bracing on the measured buildings proved to be
substantial, so that for the bending stress verification the governing eigenmode corre-
sponded to a superposition of global and local imperfections (multiwave over the beam
length; 0.69 ≤ lef,m / apurlins = effective length / distance between purlins ≤ 1.61).
In consultation with structural engineers, the assumption of combined global and local
equivalent imperfections similar to Figure 3.2 seems to be too complex for design cal-
culations. Therefore, for the calculations with equivalent imperfections (model 3), only
global equivalent bow and twist imperfections (no local ones) were assumed (Figure
3.2). The differences in the load-bearing behaviour between model 2 and model 3 thus
also include the influence of local imperfections between the application points of the
purlins. The amplitudes of the global equivalent imperfections were chosen so that the
area integral of the equivalent imperfections over the beam length corresponded to
the area integral of the measured imperfections.
3.3.2 Equivalent imperfections
Table 3.1 illustrates the summarised results of the numerical calculations of the 139
beams. It can be demonstrated that with the chosen approach for the equivalent im-
perfections (model 3), almost identical utilisations μx = σx / fm,k have been determined
with computations considering measured imperfections (model 2). The mean utilisa-
tion μx,Mz (caused by bending moments around the weak axis Mz) is approximately 15 %
smaller in model 3 than in model 2, which is due to the neglect of local imperfections.
However, since the share of utilisation μx,Mz in the total utilisation μx is a maximum of
26 %, this is not significant. In general, the assumed equivalent imperfections are well
suited to represent the load-bearing behaviour of the measured beams for bending.
Table 3.1. Numerically for 139 beams determined mean, min, max and COV values of the relative
slenderness ratio λrel,m and the maximum utilisation of the bending stress in x-direction μx, utilisation
separated for the contributions of My and Mz.
λrel,m
Model 2
Model 3
μx = σx / fm
μx,My
μx,Mz
μx = σx / fm
μx,My
μx,Mz
Mean
0.79
1.00
0.94
0.06
0.99
0.94
0.05
Minimum
0.52
1.00
0.77
0.01
0.90
0.77
0.01
Maximum
1.01
1.00
0.99
0.23
1.05
0.99
0.26
COV
0.16
0.00
0.05
0.84
0.02
0.05
0.94
Figure 3.3 and Figure 3.4 display the frequency distributions of the absolute values of
the equivalent bow and twist imperfections ey / L and eϑ x H / L. A folded normal dis-
tribution represents a good approximation of the density functions. The 95 % quantile
values of the equivalent imperfections are:
95 % quantile: ey / L = 1.19 mm/m L / 840 (bow imperfections)
eϑ x H / L = 0.76 mm/m L / 1320 (twist imperfections)
3.3.3 Torsional moment at the supports
Figure 3.5 presents the maximum torsional moments Mx at the supports per building
determined using model 2 (Mx,measured) and model 3 (Mx,equivalent) with measured or
equivalent imperfections. In addition, the diagram contains calculation results accord-
Figure 3.3. Frequency distribution of the compu-
ted equivalent bow imperfections ey in relation to
the beam span L of 139 glulam beams.
Figure 3.4. Frequency distribution of the compu-
ted equivalent twist imperfections eϑ x H (beam
height) in relation to the beam span L of 139
glulam beams.
Figure 3.5. Numerically, according to DIN EN 1995-1-1/NA (2013) and (KUHLMANN & HOFMANN (2016))
determined maximum torsional moments Mx at the supports, per building, normalised to Md / 80.
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
relative frequency [-]
ey/ L [mm/m]
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
L/1000
L/500
L/ 840
folded normal distribution
0.00
0.05
0.10
0.15
0.20
0.25
relative frequency [-]
eϑx H / L [mm/m]
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
L/500
L/1320
L/1000
folded normal distribution
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
012345678910 11 12 13
Mx/ (Md/ 80) [-]
Md/ 80
M
x,measured
M
x,equivalent
Mx,Hofmann
M
d
/ 80
2020-KW23
2020-
KW47
2020-
KW33
2020-
KW38_2
2020-
KW27
2020-
KW32
2020-
KW45_1.1
2020-
KW45_1.2
2020-
KW38_1.2
2020-
KW38_1.3
2020-
KW38_1.4
2020-
KW34
saddle roof girders
increase of H / B
fish-bellied
roof girders
increase of
H / B
parallel chord girders
increase of H / B
Eccentric
ridge with
strongly
curved lower edge
ing to the design approach in DIN EN 1995-1-1/NA (2013) with Mx = Md / 80 and the
results of the approaches (Mx,Hofmann) proposed by (KUHLMANN & HOFMANN (2016)). The
data in Figure 3.5 are sorted by the beam shape and the ratio of beam height to width
H / B and for comparability normalised to Md / 80.
The major differences between Mx,measured/equivalent and Mx,Hofmann result from the differ-
ent imperfection assumptions. According to EN 1995-1-1 (2004), bow imperfections of
ey = L/400 + L/500 were assumed in (KUHLMANN & HOFMANN (2016)), whereas the maxi-
mum measured bow imperfection was ey = L/578 (2020-KW45_1.1). This is also re-
flected in the difference at building 2020-KW45_1.1 between Mx,measured and Mx,Hofmann,
which is approximately a factor of 2.
Compared to Md / 80, the more accurate approaches of (KUHLMANN & HOFMANN (2016))
and the numerical calculations presented here take into account the influence of the
beam shape and the cross-sectional ratio H / B.
It is evident that the imperfection assumptions in the current approaches for Mx are
conservative. A revision of the design rules based on the generated database of meas-
ured imperfections and the more accurate approaches of (KUHLMANN & HOFMANN
(2016)) is recommended.
4 Summary and outlook
The assembly tolerances have a decisive influence on the design of roof structures with
slender glulam beams, yet there is a lack of sufficient data regarding these structures.
Chapter 2 reports on the results of imperfection measurements on 13 roof structures
with 139 glulam beams as part of the research project DIBt - ZP 52-5-13.194 (KUHLMANN
& TÖPLER (2021 b)). The measured horizontal bow imperfections ey of the beams were
always smaller than L/400 assumed in EN 1995-1-1 (2004) and in 87 % of the cases
smaller than L/1000. Likewise significant twist imperfections eϑ around the longitudinal
axis could be determined for most of the beams. The horizontal displacement from the
upper edge to the lower edge of a beam was on average eϑ x H = 0.0005 x L. Twist im-
perfections eϑ of beams with fork bearings designed as reinforced concrete pockets
were generally larger than with fork bearings made of timber.
It is demonstrated in Chapter 3 by numerical calculations on the 139 measured glulam
beams that, assuming sinusoidal equivalent imperfections where the area integral cor-
responds to the one of the measured imperfections, very similar load-bearing capaci-
ties can be determined numerically, compared to calculations with measured imper-
fections. This may form the basis of recommended values for the new Eurocode 5.
Additionally, it should be emphasised that the stiffness of the horizontal bracing of the
girders, as well as the fork bearings, have a decisive influence on the load-bearing be-
haviour (KUHLMANN & HOFMANN (2016)).
The evaluation of the measurement results will continue. In addition to the completion
of the evaluation shown in this paper, other possibly systematic effects such as the
assembly procedure, the bracing system, the beam shape, a group effect of several
parallel girders, the long-term behaviour and material scatter will be investigated. Pos-
sible recommendations will also concern the reduction of tolerances in execution.
5 Acknowledgements
The research project (P 52-5- 13.194-2048/19) is supervised by Deutsches Institut für
Bautechnik (DIBt) and carried out with financial support from the Federal States. This
support is gratefully acknowledged. Furthermore, the research is partially supported
by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Ger-
many´s Excellence Strategy EXC 2120/1 390831618.
Moreover, we thank Architekturbüro Rohloff & Wespel, Egger + Ingenieure GmbH,
GMS Partner AG, GöSta Hallenbau GmbH, Haas Fertigbau GmbH, Implenia Schweiz AG,
Pollmeier Massivholz GmbH & Co. KG, Schaffitzel Holzindustrie GmbH & Co. KG and
WIEHAG GmbH (in alphabetical order) for allowing measurements of the assembly tol-
erances on selected timber buildings.
Many thanks to the Institute for Photogrammetry (IfP) at the University of Stuttgart
and especially to Lena Joachim and Edward Necşulescu for carrying out the laser scan-
ning and advising on the measurements’ evaluation.
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onsannahmen und Montageregeln der DIN EN 1995-1-1 für Nagelplattenkonstrukti-
onen zur Steigerung ihrer Sicherheit und Wirtschaftlichkeit (in German). Research
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Kessel, M. H. & Sieder, M. & Kreuzinger, H. (2020): Personal contribution by Martin H.
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bridge. CEN/TC 250/SC 5/WG 3 N 153.
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gern variabler Höhe für das Torsionsmoment aus Kippstabilisierung (in German). IGF
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Kuhlmann, U. & Hofmann, R. (2016): Simplified method to determine the torsional mo-
ment due to lateral torsional buckling. INTER, 49-10-2, Graz, Institute of Structural
Design, University of Stuttgart.
Kuhlmann, U. & Töpler, J. (2021 a): Analytical and numerical investigations on imper-
fection-sensitive timber members subjected to combined bending and axial com-
pression. WCTE 2021, Institute of Structural Design, University of Stuttgart.
Kuhlmann, U. & Töpler, J. (2021 b): Imperfektionsmessungen an stabilitätsgefährdeten
Holzbauteilen - Zwischenbericht (in German). Research report, DIBt P 52-5- 13.194-
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Kuhlmann, U. & Töpler, J. & Gauß, J. & Buchholz, L. (2021): Integrated approach of
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cellence “Integrative Computational Design and Construction for Architecture”
(IntCDC), EXC 2120/1 390831618, Institute of Structural Design, University of
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feuchtigkeit (in German). Dissertation, Ruhr University Bochum.
prEN 1993-1-14 (14 April 2021): Eurocode 3: Design of steel structures Part 1-14:
Design assisted by finite element analysis (draft version). CEN/TC 250/SC 3/WG 22 N
32.
... They provide the designing structural engineer with simple and sufficiently accurate design formulas, which however are based on different assumptions for the imperfections. The imperfection assumptions are currently investigated in a DIBt project at the Institute of Structural Design [13]. However, there are only few experimental investigations and no full-scale tests on slender timber members subjected to combined bending and compression prone to lateral torsional buckling known. ...
... where My = bending moment around the y-axis (Figure 2), Nx = normal force (tension positive, Figure 2), δ = Dischinger-coefficient taking into account the distribution of My, ey/z/ϑ = sinusoidal imperfections (Figure 3), Ix/y/z = moments of inertia (Equations (13) to (16)), E = Young's modulus Em, G = shear modulus Gxz, Lc,y/z/m,ef = effective lengths under consideration of bending and normal force. The derivation of the equations is based on following assumptions [10]: ...
... maining polygonal cross-section area ( Figure 7) can be determined according to Equations (13) to (16) [16]. ...
Conference Paper
Full-text available
The verification of slender timber members at risk of lateral torsional buckling is one of the basic verifications in timber design. However, latest investigations have shown that the design formulas provided in Eurocode 5 for imperfection-sensitive members subjected to combined bending and compression tend to be conservative and more advanced verification methods are needed. Analytical and numerical models are presented that allow for the consideration of the geometrically and materially nonlinear behaviour as well as of the size effect of tensile strength ft,0 for Nx-My-Mz interaction. These models and calculation results increase the understanding of the main influencing parameters of the load-bearing capacity of imperfection-sensitive timber beams and columns and may be the basis of a revision of the current design formulas provided in EN 1995-1-1.
... Alle Verfahren liefern brauchbare Ergebnisse, wobei bei Verfahren C und D die Differenzen der Ausnutzung μx zwischen Modell 2 und 3 am geringsten sind. Ergebnisse mit Verfahren A werden in [24] präsentiert. ...
... In Abb. 24 ...
Technical Report
Full-text available
Die Holztragwerke von 23 Bauvorhaben wurden mit einem Laserscanner vermessen und die Daten von 202 BSH Bindern, 38 Buchen-Furnierschichtholz Bindern und 57 Buchen FSH Stützen in Bezug auf die Montagegenauigkeit und Imperfektionen ausgewertet. Die Messungen wurden direkt nach Montage und Ausrichten der Tragwerke durchgeführt. Für alle gemessenen Imperfektionen galt, dass die Bemessungsansätze nach EN 1995-1-1 auf der sicheren Seite liegen. Zur Ermittlung von Ersatzimperfektionen wurden numerische Vergleichsberechnungen mit Abaqus CAE/2020 durchgeführt. Die Ersatzimperfektionen wurden in Form einer Sinushalbwelle angenommen. Die 95 % Quantilwerte der Vorverformungen wurden ausgewertet und daraus abgeleitete konsistente Bemessungsempfehlungen für Ersatzimperfektionen für die Stabilitätsnachweise nach EN 1995-1-1 angegeben. Die Messdaten sind unter folgendem Link veröffentlicht: https://doi.org/10.18419/darus-3304
Conference Paper
Full-text available
The verification of slender timber members at risk of lateral torsional buckling is one of the basic verifications in timber design. However, latest investigations have shown that the design formulas provided in Eurocode 5 for imperfection-sensitive members subjected to combined bending and compression tend to be conservative and more advanced verification methods are needed. Analytical and numerical models are presented that allow for the consideration of the geometrically and materially nonlinear behaviour as well as of the size effect of tensile strength ft,0 for Nx-My-Mz interaction. These models and calculation results increase the understanding of the main influencing parameters of the load-bearing capacity of imperfection-sensitive timber beams and columns and may be the basis of a revision of the current design formulas provided in EN 1995-1-1.
Bracing of the main girder of a pedestrian bridge
  • M H Kessel
  • M Sieder
  • H Kreuzinger
Kessel, M. H. & Sieder, M. & Kreuzinger, H. (2020): Personal contribution by Martin H. Kessel, Mike Sieder and H. Kreuzinger (DE): Bracing of the main girder of a pedestrian bridge. CEN/TC 250/SC 5/WG 3 N 153.
Simplified method to determine the torsional moment due to lateral torsional buckling. INTER, 49-10-2
  • U Kuhlmann
  • R Hofmann
Kuhlmann, U. & Hofmann, R. (2016): Simplified method to determine the torsional moment due to lateral torsional buckling. INTER, 49-10-2, Graz, Institute of Structural Design, University of Stuttgart.
Research project RP 7, DFG Cluster of Excellence "Integrative Computational Design and Construction for Architecture
  • U Kuhlmann
  • J Töpler
  • J Gauß
  • L Buchholz
Kuhlmann, U. & Töpler, J. & Gauß, J. & Buchholz, L. (2021): Integrated approach of testing and numerical verifications (IATN). Research project RP 7, DFG Cluster of Excellence "Integrative Computational Design and Construction for Architecture" (IntCDC), EXC 2120/1 -390831618, Institute of Structural Design, University of Stuttgart, ongoing.
Eurocode 3: Design of steel structures -Part 1-14: Design assisted by finite element analysis (draft version)
  • F.-H Neuhaus
Neuhaus, F.-H. (1981): Elastizitätszahlen von Fichtenholz in Abhängigkeit der Holzfeuchtigkeit (in German). Dissertation, Ruhr University Bochum. prEN 1993-1-14 (14 April 2021): Eurocode 3: Design of steel structures -Part 1-14: Design assisted by finite element analysis (draft version). CEN/TC 250/SC 3/WG 22 N 32.