reliability of unreinforced masonry bracing walls · 2012. 4. 2. · din 1055-100. there, a value...

15th International Brick and Block

Masonry Conference

Florianoacutepolis ndash Brazil ndash 2012

RELIABILITY OF UNREINFORCED MASONRY BRACING WALLS

Brehm Eric1 Lissel Shelley L

2

1 Dr-Ing Forensic Engineer TUumlV SUumlD Munich Germany ericbrehmtuev-suedde

2PhD Associate Professor Dept of Civil Engineering University of Calgary sllisselucalgaryca

Bracing walls are essential members in typical masonry structures However design checks

are only performed rarely in Germany The reason for this is a paragraph in the German

design code DIN 1053-1 which allows for neglecting of this design check This mentioned

paragraph is based on construction methods different from the current state of the art

Additionally design codes have mostly been calibrated on the basis of experience

Consequently the provided level of reliability remains unknown

In this paper a systematic analysis of the provided level of reliability is conducted Analytical

models for the prediction of the shear capacity of the walls are analyzed and assessed with test

data to identify the most realistic model A complete stochastic model is developed and the

reliability of typical bracing walls is determined The difference between the theoretical level

of reliability and the ldquoactualrdquo level of reliability is evaluated taking into account the realistic

utilization of the walls Subsequently the derived level of reliability is presented and

assessed

Keywords reliability masonry target reliability probabilistic

INTRODUCTION

The key objective in structural design is the design of sufficiently safe and reliable structures

While safety commonly refers to the absence of hazards reliability is a quantifiable value and

can be determined by probabilistic methods In current structural design codes the demands

of safety are incorporated through the use of partial safety factors which can be derived from

probabilistic analysis Unlike other materials in construction the reliability of masonry

members has not been subjected to extensive research in the past Recent research (see

Glowienka (2007)) showed the necessity for a probabilistic approach to masonry structures

However most studies are focussed on masonry subjected to axial stress and flexure Since

masonry shear walls exhibit a much more complex load-carrying behaviour and are even

more important to structural integrity this paper focuses on masonry shear walls subjected to

wind loading The structural reliability of these walls will be analysed by assessing different

analytical models and probabilistic modelling

RELIABILITY OF STRUCTURES

The most important requirement for structures is reliability The term reliability concerns

every aspect of a structure structures have to be reliable when it comes to load bearing

capacity as well as serviceability In design every parameter is uncertain to some extent The

uncertainty may be in the strength of materials as well as in dimensions and quality of

workmanship All parameters further referred to as basic variables influence the properties of


Masonry Conference


a member Reliability is linked to the probability that a member will exceed a certain limit

state This can be described by so called limit state functions which can be written as in

Eq (1)

Z(RE) = R - E (1)

where R is the resistance and E is the load effect

In the case where R = E the ultimate limit state is reached It can be seen from this equation

that the safety of a member can be defined as the difference between the resistance and the

load effect It has to be noted that R and E are independent random variables in many cases

so they have to be described by means of stochastics Therefore a stochastic model mostly

consisting of a probability distribution and the corresponding moments (eg mean standard

deviation) is required for every basic variable Figure 1 presents this for the simplified two-

dimensional case

Figure 1 Definition of failure probability (Glowienka (2007))

The failure probability can be computed by probabilistic methods such as SORM (Second

Order Reliability Method) or Monte Carlo-simulation For further information see

Rackwitz (2004)

For the description of the resistance appropriate models are required that describe the load

carrying behaviour realistically Contrary to design models a model that underestimates the

load carrying behaviour is not appropriate for probabilistic analysis

To find a measure for reliability that can be defined independently from the type of

distribution of the basic variables the reliability index βR according to Cornell (1969) has

proven useful see Eq (2) The major advantage of this definition is that only the mean mz

and standard deviation z of the basic variables need to be known

Z

ZR

m

(2)

load effect E

resistance R safety margin

failure

probability Pf


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With this measure target reliabilities can be defined Ideally target reliabilities are based on a

complex optimization process accounting for aspects of safety as well as economic

requirements In the past target reliability has mostly been determined on an empirical basis

Since the target reliability has a major influence on safety factors setting too large of a target

reliability will lead to uneconomic design More information can be found in Brehm (2011)

GruSiBau (1981) and Rackwitz (2004)

The Joint Committee on Structural Safety (JCSS) gives the target reliabilities depending on

the failure consequences as shown in Table 1

Table 1 Target reliabilities according to JCSS (2001) for an observation period of 50

years

Relative cost for

enhancing the structural

reliability

Failure consequences

Minora)

Averageb)

Majorc)

large β=17 (Pf ∙510-2

) β=20 (Pf ∙3∙10-2

) β=26 (Pf 510-3

)

medium β=26 (Pf 510-3

) β=32 (Pf 710-4

)d)

β=35 (Pf 3∙10-4

)

small β=32 (Pf ∙710-4

) β=35 (Pf 3∙10-4

) β=38 (Pf 10-5

) a)

eg agricultural building b)

eg office buildings residential buildings or industrial buildings c)

eg bridges stadiums or high-rise buildings d)

recommendation for regular cases according to JCSS 2001

These target reliabilities are considered to be sufficient for most cases and will be taken as

reference for further calculations Another recommendation is given by the German code

DIN 1055-100 There a value of βtarget = 38 is given for a 50 year observation period

A full probabilistic approach for design is difficult since stochastic models have to be known

for all basic variables and good prediction models are required To simplify design the semi-

probabilistic partial safety concept is applied in most design codes In this concept the partial

safety factors for different basic variables make it possible to account for different scatter of

the variables A typical application of partial safety factors is presented by the following

equation

R

E

RE

(3)

where E is the load effect and R is the resistance both are usually defined as characteristic

values The safety factors which are greater than unity are represented by γi

LOAD-CARRYING BEHAVIOUR OF URM BRACING WALLS

To be able to determine the resistance and capacity of a member the load-carrying behaviour

has to be known Masonry members subjected to shear exhibit a complex load-carrying

behaviour There is however a general consensus on the 3 main in-plane failure modes in

masonry which include flexural failure (tension at the heel or crushing at the toe) sliding

failure in one or multiple bed joints and diagonal tensile failure of the panel which may be

combined with sliding failure of the joints Cracks are typically diagonal and stepped in nature

but may also transverse through units as shown in Figure 2


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Figure 2 Typical failure modes for in-plane shear failure of masonry

Many models have been developed in the past for the prediction of the shear capacity of

Unreinforced Masonry (URM) walls In this study a variety of models was compared to test

data aiming at the identification of the most realistic model For further information on the

load-carrying behaviour of masonry shear walls and shear models see Kranzler (2008)

STRUCTURAL MODEL

To apply the different shear models and to assess the test data an appropriate structural model

is required The model is considered appropriate if it allows for the modelling of a large

number of walls with variation of only a few parameters and takes into account the coupling

moments of the concrete slabs Such a model has been proposed by Kranzler (2008) and is

presented in Figure 3 The shear slenderness v can then be computed from Eq (4)

Figure 3 Structural Model

(4)

SHEAR CAPACITY PREDICTION MODEL UNCERTAINTIES

The previously mentioned structural model was combined with a number of prediction

models to assess a test database The goal was the determination of the uncertainties linked to

Tension Crushing

(a) (b) (c)

Diagonal Tension

(a) (b) (c)

Sliding


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the different prediction models to finally be able to identify the most accurate model This

model should then be used for the analysis of the reliability of the walls

To achieve more realistic results and to eliminate stochastic uncertainties a Bayesian update

has been performed taking into account prior information This prior information mainly

consisted of expert opinions found in the literature More information on this can be found in

Rackwitz (2004)

In Table 2 the results in form of the mean and scatter of the test-to-prediction ratio are

presented for Calcium Silicate (CS) Autoclaved Aerated Concrete (AAC) and Clay Brick

(CB) walls For detailed information about the different models please see Brehm (2011)

Table 2 Stochastic moments of test-to-prediction ratios for different models after

Bayesian Update

Failure mode Model Unit m CoV

Diagonal

tension

Mann amp Muumlllera

CS 121 025 21

AAC 112 022 20

CB 140 023 16

DIN EN 1996-1-1NA

CS 115 028 24

AAC 114 020 18

CB 103 018 18

Kranzler

CS 112 030 27

AAC 117 027 23

CB 099 019 19

DIN 1053-100

CS 123 027 22

AAC 115 030 26

CB 139 023 16

Sliding shear

Mann amp Muumlllera

CS 127 021 17

AAC 123 024 19

CB 141 024 17

DIN EN 1996-1-1NA

CS 115b 024 21

AAC 121b 025 20

CB 124 024 20

DIN 1053-100

CS 115 022 19

AAC 112 027 23

CB 140 024 17

Flexure ideal-plastic

CS 100 018 18

AAC 105 016 15

CB 110 020 18 aideal-plastic stress-strain relationship

bupdated with a mean of 10 (Likelihood)

It was found that every model performed differently depending on unit material and possible

failure mode Thus just a single ldquomost appropriate modelrdquo could not be determined

Therefore a combination of models was chosen for the most realistic representation of the

behaviour of masonry subjected to in-plane shear The corresponding model uncertainties are

summarized in Table 3


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Table 3 Model uncertainties

Failure mode Unit Model Dist m CoV

Diagonal tension Θdt

CS Mann amp Muumlller

LN

121 025 21

AAC DIN EN 1996-1-1NA

114 020 17

CB 103 018 17

Sliding shear Θs

CS DIN EN 1996-1-1NA 115 024 21

AAC Mann amp Muumlller 123 024 20

CB DIN EN 1996-1-1NA 124 024 19

Flexure Θf

CS

fully-plastica

100 018 18

AAC 105 016 15

CB 110 020 18

Shear crushing Θc all DIN EN 1996-1-1NA 100 020 20 astress-strain relationship

STOCHASTIC MODEL

For the reliability analysis every significant basic variable has to be modelled as a random

variable In this study every parameter related to shear design of masonry walls subjected to

wind load has been assessed thoroughly to obtain the relevant stochastic moments Note that

these variables are related to both sides of the limit state function resistance and loads A

summary of the stochastic model is presented in Table 4 Note that the model uncertainties for

the resistance are displayed in Table 3 The model uncertainties are modelled differently for

every unit material and failure mode according to the previously presented assessment of the

test database

Table 4 Stochastic model

Basic variable Material Distr mXiXki CoV

Res

ista

nce

Compressive strength of masonry fm

CS

LN

155 19

AAC 181 16

CB 143 17

Tensile strength of unit fbt

CS 184 26

AAC 155 16

CB 131 24

Cohesion fv0 TLM 214 35

GPM 357 40

Friction Coefficient all 133 19

Load

Model uncertainty on the shear load Ev

all

100 10

Model uncertainty on the axial load Ea 100 5

Wind load vab

Weibull 103 7

Live load nQa Gumbel 110 20

Dead load nG N 100 6 aobservation period of 50 yrs

b = 0073


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RELIABILITY ANALYSIS

The reliability analysis has been performed for selection of over 400 walls which were

previously designed according to German design codes This made it possible to determine

the realistically provided reliability of shear walls in Germany

The reliability has been determined by SORM Basically the failure probability for every

possible failure mode for every wall has been determined and then the obtained failure

probabilities for every failure mode have been summed up Since one failure mode clearly

always governs the analysis the effects of possible overlap are small (lt 1) Figure 4

illustrates the determination of the failure probability By applying this method time-

consuming Monte-Carlo-Simulation could be avoided The reliability of the walls was

determined for full utilization of the cross-section to model walls in ultimate limit state and to

obtain comparable results for the different unit materials

Figure 4 Approach for Probabilistic Analysis

RESULTS THEORETICAL RELIABILITY

It quickly became obvious that the walls do not fulfil the code requirements in terms of target

reliability when the examined walls were slender Squat walls however reached very large

values of the reliability Note that every wall assumed to be 100 utilized

The reason for the differences in reliability between slender and squat walls is the

eccentricity Slender walls reach a much larger eccentricity than squat walls In the following

the axial and shear loads according to Eq (5) and Eq (6) will be used

mw

Gk

Gkflt

Nn

(5)

mw

Ek

Ekflt

Vv

(6)


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where fm is the masonry compressive strength NGk is the axial dead load and VEk is the shear

load

Figure 5 shows the reliability and eccentricity for a slender CS wall related to the axial dead

load nGk

Figure 5 Reliability vs Eccentricity for a slender CS wall (v = 30) and full utilization

of the cross-section (100)

In general a large eccentricity leads to small reliability In Figure 6 the reliability for a squat

CB wall is shown It can be seen that the reliability is consistently very high and above the

target region

Figure 6 Reliability vs Eccentricity for a squat CB wall (v = 05) and full utilization of

the cross section (100)

Figure 7 shows a comparison of the reliabilities obtained for different unit materials and

slender walls It can be seen that the reliabilities are similarly distributed and stay below the

target values The larger reliability for AAC walls is due to a peculiarity in the German code

DIN 1053-1 where the tensile strength of AAC units was massively underestimated


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Figure 7 Reliability of slender masonry walls for different materials (v = 30) and full

utilization of the cross section (100)

RESULTS ACTUAL RELIABILITY

The reliabilities obtained for slender walls are small much smaller than one would expect

considering the fact that there are actually no structural failures of masonry shear walls due to

wind load reported The most likely reason for this is the low actual level of utilization in

reality In this study every wall was designed for full utilization However CS and CB walls

provide much larger strength than AAC walls so that higher loads are required to reach full

utilization The wind load acting on a structure in reality will be more or less the same no

matter which material is used Thus levels of utilization are different for every unit material

The typical effect is shown in Figure 8

Figure 8 Reliability vs Eccentricity for a slender CS wall (v = 30) and different

utilization levels of the cross section


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To assess this effect a typical town house was modelled using FE software Different unit

materials were investigated and the actual level of utilization due to wind and axial load was

determined for every wall Subsequently the reliability taking into account the actual level of

utilization has been determined It was found that the reliability reaches similar values for

every wall material and that these values are significantly higher than the theoretical values of

reliability The results are summarized in Table 5

The ldquoactualrdquo value of reliability determined on the basis of DIN 1053-1 does not reach the

target values of DIN 1055-100 Nonetheless it matches the recommendations of JCSS (2001)

see Table 1 However the target values have to be analysed and assessed since there is no

difference in target reliability depending on the failure consequences linked to a structure

These values are valid for a skyscraper as well as for agricultural buildings In a future study

a full-probabilistic optimization of typical masonry structures will be conducted to determine

the socio-economic optimum target reliability for masonry structures

Table 5 Results for average theoretical and actual reliability

Material

Average reliability index provided

in common masonry constructiona

theoreticalb

actualc

DIN 1053-1 DIN 1053-100 DIN EN 1996-1-1NA

CS (20TLM) 20 27 26 32d

CB (12GPM IIa) 21 30 30 31e

AAC (4TLM) 30 37 33 30f

acorresponding to v = 30 and nGk = 00502

bfull (100) utilization of the wall

cdetermined on the basis of DIN 1053-1

dcorresponding to a utilization of 70

ecorresponding to a utilization of 80

fcorresponding to a utilization of 100

SUMMARY

The reliability of masonry shear walls subjected to wind loading has been determined The

walls were designed according to German design codes so that the provided level of reliability

in Germany could be derived It was shown that the theoretical reliability of slender masonry

walls falls short of the target values of DIN 1055-100 if full utilization of the cross-section is

assumed For realistic values of the utilization reliability is much larger and the three

investigated unit materials reach similar values

REFERENCES

Brehm E rdquoReliability of Unreinforced Masonry Bracing Walls ndash Probabilistic Approach and

Optimized Target Valuesrdquo Doctoral Thesis Technische Universitaumlt Darmstadt Darmstadt

Germany 2011

Cornell CA rdquoA reliability-based structural coderdquo ACI Journal Vol 66 No 12 1969


Masonry Conference


Glowienka S rdquoZuverlaumlssigkeit von Mauerwerkswaumlnden aus groszligformatigen Steinenrdquo

Doctoral Thesis Technische Universitaumlt Darmstadt Darmstadt Germany 2007

GruSiBau rdquoGrundlagen zur Festlegung von Sicherheitsanforderungen fuumlr bauliche Anlagenrdquo

NA Bau Beuth Verlag Berlin Germany 1981

Joint Committee on Structural Safety (JCSS) rdquoProbabilistic Assessment of Existing

Structuresrdquo RILEM publucations SARL 2001

Kranzler T rdquoTragfaumlhigkeit uumlberwiegend horizontal beanspruchter Aussteifungsscheiben aus

unbewehrtem Mauerwerkrdquo Doctoral Thesis Technische Universitaumlt Darmstadt Darmstadt

Germany 2008

Mann W Muumlller H rdquoSchubtragfaumlhigkeit von Mauerwerkrdquo in Mauerwerk-Kalender 3

Ernst amp Sohn Berlin 1978

Rackwitz R rdquoZuverlaumlssigkeit und Lasten im konstruktiven Ingenieurbaurdquo Technical

University of Munich Munich Germany 2004


Masonry Conference


a member Reliability is linked to the probability that a member will exceed a certain limit

state This can be described by so called limit state functions which can be written as in

Eq (1)

Z(RE) = R - E (1)

where R is the resistance and E is the load effect

In the case where R = E the ultimate limit state is reached It can be seen from this equation

that the safety of a member can be defined as the difference between the resistance and the

load effect It has to be noted that R and E are independent random variables in many cases

so they have to be described by means of stochastics Therefore a stochastic model mostly

consisting of a probability distribution and the corresponding moments (eg mean standard

deviation) is required for every basic variable Figure 1 presents this for the simplified two-

dimensional case

Figure 1 Definition of failure probability (Glowienka (2007))

The failure probability can be computed by probabilistic methods such as SORM (Second

Order Reliability Method) or Monte Carlo-simulation For further information see

Rackwitz (2004)

For the description of the resistance appropriate models are required that describe the load

carrying behaviour realistically Contrary to design models a model that underestimates the

load carrying behaviour is not appropriate for probabilistic analysis

To find a measure for reliability that can be defined independently from the type of

distribution of the basic variables the reliability index βR according to Cornell (1969) has

proven useful see Eq (2) The major advantage of this definition is that only the mean mz

and standard deviation z of the basic variables need to be known

Z

ZR

m

(2)

load effect E

resistance R safety margin

failure

probability Pf


Masonry Conference











years

Relative cost for


reliability


Minora)

Averageb)

Majorc)

large β=17 (Pf ∙510-2

) β=20 (Pf ∙3∙10-2

) β=26 (Pf 510-3

)


) β=32 (Pf 710-4

)d)

β=35 (Pf 3∙10-4

)

small β=32 (Pf ∙710-4

) β=35 (Pf 3∙10-4

) β=38 (Pf 10-5

) a)













equation

R

E

RE

(3)












Masonry Conference







STRUCTURAL MODEL







(4)




Tension Crushing

(a) (b) (c)

Diagonal Tension

(a) (b) (c)

Sliding


Masonry Conference







Rackwitz (2004)





Bayesian Update


Diagonal

tension

Mann amp Muumlllera

CS 121 025 21

AAC 112 022 20

CB 140 023 16

DIN EN 1996-1-1NA

CS 115 028 24

AAC 114 020 18

CB 103 018 18

Kranzler

CS 112 030 27

AAC 117 027 23

CB 099 019 19

DIN 1053-100

CS 123 027 22

AAC 115 030 26

CB 139 023 16

Sliding shear

Mann amp Muumlllera

CS 127 021 17

AAC 123 024 19

CB 141 024 17

DIN EN 1996-1-1NA

CS 115b 024 21

AAC 121b 025 20

CB 124 024 20

DIN 1053-100

CS 115 022 19

AAC 112 027 23

CB 140 024 17


CS 100 018 18

AAC 105 016 15









Masonry Conference






LN

121 025 21


114 020 17

CB 103 018 17

Sliding shear Θs

CS DIN EN 1996-1-1NA 115 024 21


CB DIN EN 1996-1-1NA 124 024 19

Flexure Θf

CS

fully-plastica

100 018 18

AAC 105 016 15

CB 110 020 18


STOCHASTIC MODEL








test database



Res

ista

nce


CS

LN

155 19

AAC 181 16

CB 143 17


CS 184 26

AAC 155 16

CB 131 24


GPM 357 40


Load


all

100 10


Wind load vab

Weibull 103 7



b = 0073


Masonry Conference






















mw

Gk

Gkflt

Nn

(5)

mw

Ek

Ekflt

Vv

(6)


Masonry Conference



load


load nGk





target region








Masonry Conference
















Masonry Conference
















Material



theoreticalb

actualc

DIN 1053-1 DIN 1053-100 DIN EN 1996-1-1NA

CS (20TLM) 20 27 26 32d

CB (12GPM IIa) 21 30 30 31e

AAC (4TLM) 30 37 33 30f







SUMMARY







REFERENCES



Germany 2011



Masonry Conference










Germany 2008






Masonry Conference











years

Relative cost for


reliability


Minora)

Averageb)

Majorc)

large β=17 (Pf ∙510-2

) β=20 (Pf ∙3∙10-2

) β=26 (Pf 510-3

)


) β=32 (Pf 710-4

)d)

β=35 (Pf 3∙10-4

)

small β=32 (Pf ∙710-4

) β=35 (Pf 3∙10-4

) β=38 (Pf 10-5

) a)













equation

R

E

RE

(3)












Masonry Conference







STRUCTURAL MODEL







(4)




Tension Crushing

(a) (b) (c)

Diagonal Tension

(a) (b) (c)

Sliding


Masonry Conference







Rackwitz (2004)





Bayesian Update


Diagonal

tension

Mann amp Muumlllera

CS 121 025 21

AAC 112 022 20

CB 140 023 16

DIN EN 1996-1-1NA

CS 115 028 24

AAC 114 020 18

CB 103 018 18

Kranzler

CS 112 030 27

AAC 117 027 23

CB 099 019 19

DIN 1053-100

CS 123 027 22

AAC 115 030 26

CB 139 023 16

Sliding shear

Mann amp Muumlllera

CS 127 021 17

AAC 123 024 19

CB 141 024 17

DIN EN 1996-1-1NA

CS 115b 024 21

AAC 121b 025 20

CB 124 024 20

DIN 1053-100

CS 115 022 19

AAC 112 027 23

CB 140 024 17


CS 100 018 18

AAC 105 016 15









Masonry Conference






LN

121 025 21


114 020 17

CB 103 018 17

Sliding shear Θs

CS DIN EN 1996-1-1NA 115 024 21


CB DIN EN 1996-1-1NA 124 024 19

Flexure Θf

CS

fully-plastica

100 018 18

AAC 105 016 15

CB 110 020 18


STOCHASTIC MODEL








test database



Res

ista

nce


CS

LN

155 19

AAC 181 16

CB 143 17


CS 184 26

AAC 155 16

CB 131 24


GPM 357 40


Load


all

100 10


Wind load vab

Weibull 103 7



b = 0073


Masonry Conference






















mw

Gk

Gkflt

Nn

(5)

mw

Ek

Ekflt

Vv

(6)


Masonry Conference



load


load nGk





target region








Masonry Conference
















Masonry Conference
















Material



theoreticalb

actualc

DIN 1053-1 DIN 1053-100 DIN EN 1996-1-1NA

CS (20TLM) 20 27 26 32d

CB (12GPM IIa) 21 30 30 31e

AAC (4TLM) 30 37 33 30f







SUMMARY







REFERENCES



Germany 2011



Masonry Conference










Germany 2008






Masonry Conference







STRUCTURAL MODEL







(4)




Tension Crushing

(a) (b) (c)

Diagonal Tension

(a) (b) (c)

Sliding


Masonry Conference







Rackwitz (2004)





Bayesian Update


Diagonal

tension

Mann amp Muumlllera

CS 121 025 21

AAC 112 022 20

CB 140 023 16

DIN EN 1996-1-1NA

CS 115 028 24

AAC 114 020 18

CB 103 018 18

Kranzler

CS 112 030 27

AAC 117 027 23

CB 099 019 19

DIN 1053-100

CS 123 027 22

AAC 115 030 26

CB 139 023 16

Sliding shear

Mann amp Muumlllera

CS 127 021 17

AAC 123 024 19

CB 141 024 17

DIN EN 1996-1-1NA

CS 115b 024 21

AAC 121b 025 20

CB 124 024 20

DIN 1053-100

CS 115 022 19

AAC 112 027 23

CB 140 024 17


CS 100 018 18

AAC 105 016 15









Masonry Conference






LN

121 025 21


114 020 17

CB 103 018 17

Sliding shear Θs

CS DIN EN 1996-1-1NA 115 024 21


CB DIN EN 1996-1-1NA 124 024 19

Flexure Θf

CS

fully-plastica

100 018 18

AAC 105 016 15

CB 110 020 18


STOCHASTIC MODEL








test database



Res

ista

nce


CS

LN

155 19

AAC 181 16

CB 143 17


CS 184 26

AAC 155 16

CB 131 24


GPM 357 40


Load


all

100 10


Wind load vab

Weibull 103 7



b = 0073


Masonry Conference






















mw

Gk

Gkflt

Nn

(5)

mw

Ek

Ekflt

Vv

(6)


Masonry Conference



load


load nGk





target region








Masonry Conference
















Masonry Conference
















Material



theoreticalb

actualc

DIN 1053-1 DIN 1053-100 DIN EN 1996-1-1NA

CS (20TLM) 20 27 26 32d

CB (12GPM IIa) 21 30 30 31e

AAC (4TLM) 30 37 33 30f







SUMMARY







REFERENCES



Germany 2011



Masonry Conference










Germany 2008






Masonry Conference







Rackwitz (2004)





Bayesian Update


Diagonal

tension

Mann amp Muumlllera

CS 121 025 21

AAC 112 022 20

CB 140 023 16

DIN EN 1996-1-1NA

CS 115 028 24

AAC 114 020 18

CB 103 018 18

Kranzler

CS 112 030 27

AAC 117 027 23

CB 099 019 19

DIN 1053-100

CS 123 027 22

AAC 115 030 26

CB 139 023 16

Sliding shear

Mann amp Muumlllera

CS 127 021 17

AAC 123 024 19

CB 141 024 17

DIN EN 1996-1-1NA

CS 115b 024 21

AAC 121b 025 20

CB 124 024 20

DIN 1053-100

CS 115 022 19

AAC 112 027 23

CB 140 024 17


CS 100 018 18

AAC 105 016 15









Masonry Conference






LN

121 025 21


114 020 17

CB 103 018 17

Sliding shear Θs

CS DIN EN 1996-1-1NA 115 024 21


CB DIN EN 1996-1-1NA 124 024 19

Flexure Θf

CS

fully-plastica

100 018 18

AAC 105 016 15

CB 110 020 18


STOCHASTIC MODEL








test database



Res

ista

nce


CS

LN

155 19

AAC 181 16

CB 143 17


CS 184 26

AAC 155 16

CB 131 24


GPM 357 40


Load


all

100 10


Wind load vab

Weibull 103 7



b = 0073


Masonry Conference






















mw

Gk

Gkflt

Nn

(5)

mw

Ek

Ekflt

Vv

(6)


Masonry Conference



load


load nGk





target region








Masonry Conference
















Masonry Conference
















Material



theoreticalb

actualc

DIN 1053-1 DIN 1053-100 DIN EN 1996-1-1NA

CS (20TLM) 20 27 26 32d

CB (12GPM IIa) 21 30 30 31e

AAC (4TLM) 30 37 33 30f







SUMMARY







REFERENCES



Germany 2011



Masonry Conference










Germany 2008






Masonry Conference






LN

121 025 21


114 020 17

CB 103 018 17

Sliding shear Θs

CS DIN EN 1996-1-1NA 115 024 21


CB DIN EN 1996-1-1NA 124 024 19

Flexure Θf

CS

fully-plastica

100 018 18

AAC 105 016 15

CB 110 020 18


STOCHASTIC MODEL








test database



Res

ista

nce


CS

LN

155 19

AAC 181 16

CB 143 17


CS 184 26

AAC 155 16

CB 131 24


GPM 357 40


Load


all

100 10


Wind load vab

Weibull 103 7



b = 0073


Masonry Conference






















mw

Gk

Gkflt

Nn

(5)

mw

Ek

Ekflt

Vv

(6)


Masonry Conference



load


load nGk





target region








Masonry Conference
















Masonry Conference
















Material



theoreticalb

actualc

DIN 1053-1 DIN 1053-100 DIN EN 1996-1-1NA

CS (20TLM) 20 27 26 32d

CB (12GPM IIa) 21 30 30 31e

AAC (4TLM) 30 37 33 30f







SUMMARY







REFERENCES



Germany 2011



Masonry Conference










Germany 2008






Masonry Conference






















mw

Gk

Gkflt

Nn

(5)

mw

Ek

Ekflt

Vv

(6)


Masonry Conference



load


load nGk





target region








Masonry Conference
















Masonry Conference
















Material



theoreticalb

actualc

DIN 1053-1 DIN 1053-100 DIN EN 1996-1-1NA

CS (20TLM) 20 27 26 32d

CB (12GPM IIa) 21 30 30 31e

AAC (4TLM) 30 37 33 30f







SUMMARY







REFERENCES



Germany 2011



Masonry Conference










Germany 2008






Masonry Conference



load


load nGk





target region








Masonry Conference
















Masonry Conference
















Material



theoreticalb

actualc

DIN 1053-1 DIN 1053-100 DIN EN 1996-1-1NA

CS (20TLM) 20 27 26 32d

CB (12GPM IIa) 21 30 30 31e

AAC (4TLM) 30 37 33 30f







SUMMARY







REFERENCES



Germany 2011



Masonry Conference










Germany 2008






Masonry Conference
















Masonry Conference
















Material



theoreticalb

actualc

DIN 1053-1 DIN 1053-100 DIN EN 1996-1-1NA

CS (20TLM) 20 27 26 32d

CB (12GPM IIa) 21 30 30 31e

AAC (4TLM) 30 37 33 30f







SUMMARY







REFERENCES



Germany 2011



Masonry Conference










Germany 2008






Masonry Conference
















Material



theoreticalb

actualc

DIN 1053-1 DIN 1053-100 DIN EN 1996-1-1NA

CS (20TLM) 20 27 26 32d

CB (12GPM IIa) 21 30 30 31e

AAC (4TLM) 30 37 33 30f







SUMMARY







REFERENCES



Germany 2011



Masonry Conference










Germany 2008






Masonry Conference










Germany 2008





reliability of unreinforced masonry bracing walls · 2012. 4. 2. · din 1055-100. there, a value...

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