11 th INTERNA TIONAL BRICKJBLOCK MASONR Y CONFERENCE

TONGJI UNIVERSITY, SHANGHAI, CHINA, 14 - 160CTOBER 1997

LOAD BEARING CAP ACITY OF mSTORICAL MASONRY

Peter Warnecke1

1. ABSTRACT

The load-bearing model of multiple-leaf masonry under compression and bending introduced here, can be applied to ali types of masonry due to its modular structure. The ultimate limit state of the load-bearing capacity will be defined by ultimate limit strain states. The number, stiffness and strength of every single leaf as well as the leafbond will be taken into consideration.

2. INTRODUCTION

Historical masonry exhibits a great variety of stone material, masonry bond and masonry leaf structure. Brick masonry is known in a number of regionally typical, historical bonds. Concerning natural quarry stone masonry, the kind of masonry bond depends on the stone work. A combination ofboth bricks and natural quarry stone was also frequent.

In addition, historical brick and quarry stone masonry is marked by a multiple-leaf structure (fig. 1). There are double leaf structures with an outside, weathered masonry leaf and an interior leaf, as well as triple leaf structures that have an additional centre masonry leaf

In spite of these different types of masonry, it must be possible to develop a universally valid load-bearing model. The prerequisite for this is the modular structure of the model which facilitates the adaptation ofsingle elements ofthis model to the type ofmasonry in questiono A corresponding load-bearing model of single-leaf and multiple-leaf structures exposed to compression and bending as well as shear force will be introduced in the following. Doing this, a distinction between cohesive and non-cohesive centre masonry leaves has to be made. Cohesive centre masonry leaves have their own stiffness and stability, non-cohesive centre masonry leaves consist ofbulk material and put pressure on the externalleaves.

1 Dr.-Ing., Associate, bow consulting engineers, Breite Str. 15, 38100 Braunschweig, Germany

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100 em I 25 I 150 em 120em

- outside inside - - outside inside - -outside inside -

Fig. 1: The multiple-Ieaf structure of historical masoruy

3. DEMANDS ON THE LOAD-BEARING MODEL

In Germany, the uItimate limit state ofthe load-bearing capacity ofmasoruy is defined by an ultimate stress according to DIN 1053, part 1. A linear elastic material behaviour is presupposed, the tensile strength is neglected. By means of the eccentricity e = MIN, a simplified caL:ulation of the stress at the leaf edge of rectangular cross-sections can now be done.

This advantage ofthe simplified design concept is 10st, however, when taking other types of cross-sections into account (e. g., circular cross-sections of pillars, or T -shaped cross­sections of buttresses). Given the gaping of the joint and a multiple-leaf structure, the stress at the leaf edge can on1y be calculated iteratively.

For historical, multiple-Ieaf masoruy, the ultimate load-bearing capacity can on1y be defined using ultimate limit strain states. Subsequently, calculations have to be made on the internai force levei; this concept corresponds to the common procedure applied to reinforced concrete and steel structures (according to DIN 18800, new edition). For the definition ofultimate limit strain states, an elastic-plastic material behaviour will be used following DIN 1053, part 2, and EC 6; the compressive strength and stiffness of this material will be adapted to the masoruy structure. For the load-bearing capacity under compression and bending, a plane stmin distribution will be assumed initially. Concerning cross-sections that are subject to shear forces, the load-bearing capacity of the leaf bond has to be examined additionally.

4. FAILURE MODEL

This model describes the compressive strength of the masoruy leaf in questiono According to the type of bricks or stone and the masonry bond of the leaf, varying models are used.

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For brick masonry, Hilsdorf [2] developed a failure mo deI which is based on the difference between the respective lateral strains of brick and mortar. AlI newer mo deIs [3,4] are based on Hilsdorfs model. In spite of this, other models have gained acceptance which are not based on mechanical reasoni'1g, but on empiricaI calculations deriving the compressive strength of the masonry from the brick and mortar strength. The standard EC 6 gives the following relation for brick masonry (eq. 1):

fc,ma = 0.50 x (".tO.65 x fc,moo.

25 (1)

Given the average strength of the bricks and mortar, resp., the compressive strength of the masonry is calculated as the characteristic value.

For quany stone masonry, there are currently no empirical approaches. During recent years, however, a number of failure models have been developed in Germany [5 - 8]. Although ali models are based on mechanical observations, nevertheless they have been calibrated in accordance with the type of masonry in questiono Currently, there is no universally applicable failure model which produces equaIly accurate results for every kind of stone work and masonry bond. A comparison with our own experimentaI results shows that there can be considerable deviations [9]. It is therefore recommended to use several failure models in parallel and to employ the characteristic values of the input parameters.

For cohesive centre masonry leaves containing a high volume ofmortar, the compressive strength is calculated using a phase model (eq. 2, according to [9]).

(2)

The compressive strength of the cohesive centre masonry leaf depends on the compressive strength, the mortar content per volume, vmo, and on the cavity content of the centre masonry leaf, Vc.

5. MATERIAL MODEL

Unaffected by the type of masonry, a bilinear elastic-plastic material model according to figo 2 is used for each masonry leaf. The ultimate strain states Epl = fc,ma / Ema and Eu = 2 Epl are adapted to the mechanical properties of each masonry leaf; the tensile strength is neglected. The compressive strength is calculated using the failure model according to section 3.2, the modulus of elasticity for brick masonry is calculated according to DIN 1053, part 1, using eq. (3), for quarry stoile masonry according to [9] using eq. (4), and for cohesive centre masonry leaves (using the phase model according to [9]) using eq. 5:

Brick masonry Quarry stone masonry Intemalleaf

Ema = 1000 fema Ema = 1500 -ife,ma l/Ema = (I - vst)2/ (Emo x vmo) + V,t / E.t

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(3) (4) (5)

x I:)

11) 11) QJ '­..... 11)

fe,ma

Epl Eu

strain Ex

Fig. 2: Material model ofthe masonry leaf

6. LEAF BOND OF COHESlVE STRUCTURES

Next to the material behaviour of the individual masonry leave, the leaf bond has considerable influence on the load-bearing capacity of multiple-leaf, cohesive structures. Fig. 3 shows two ultimate limit states of the leaf bond. Assuming a fixed leaf bond, the masonry leaves are prevented from relative shlfting by shear stresses. The strain distribution is plane in every section. The fixed leaf bond facilitates the maximum load­bearing capacity, but requires hlgh shear stresses in the masonry leaf joint.

without leaf bond fixed leaf bond

Fig. 3: Multiple-Ieaf structures with a fixed or without leafbond.

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In multiple-leaf structures without masonry bond, the relative shifting of the leaves is unrestrained. At the leaf edge, fissures due to strain occur. The load-bearing capacity is the sum of the load-bearing capacitiy of each individual leave and therefore it is smaller than in the case ofa fixed leafbond.

In reality, the leaf bond will correspond to an intermediary state. This is known as a moveable leaf bond. The shear stress in the masonry leaf joint and the load-bearing capacity are smaIler than in the case of a fixed leaf bond, the relative shifting of the masonry leaves in the coping of the wall is smaIler than in the case of a bondless structure.

7. SHEAR STRENGTH OF COHESIVE STRUCTURES

The shear strength of the leaf joint depends on the physical and geometrical properties. The geometrical arrangement can be idealized by encIosing corbels (fig. 4). The interconnection between the leaves is quantified by the degree oftoothing, kt. It gives the area of the corbel Ldi x b i per m2 of the waIl area and has to be sounded at the actual building in question, or it has to be estimated. If the masonry leaf joint is plane, kt = O; if courses ofheaders and stretchers altemate regularIy, kt = 0.5 .

The shear strength of the vertical area portions of the joint is limited by mortar cohesion. It depends on the quality ofmortar in the masonry leafjoint and is taken from DIN 1053. Within the enclosing corbels, the shear strength is limited by the mortar strength. If the cavity content, V c, of the joint is further taken into account, the shear strength of the leaf joint foIlows eq. (6) :

(6)

.......... kt - Id j ·b j

- l ·b

model reality

Fig. 4: A geometrical model ofthe leafbond

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8. LOAD-BEARING CAPACITY OF COHESIVE STRUCTURES WITH FIXED LEAFBOND

Given a fixed leaf bond, a plane strain distribution may be assumed in ali sections. This requires shear stresses in the masonry leaf joint which are calculated using eq. (7) to simplity matters.

'tlh = (V X S) / (I x t) (7)

As a prerequisite for the assumption of a plane strain distribution, the shear stress from eq. (7) has to be smaller than the shear strength ofthe leafjoint.

-Mu

/ / I \ \

/ /

i

\ '''.

"-"

-

"

',\

,,/

\ \

\ \ )

/ ./

-- fixed leaf bond

_ . - without leaf bond

Fig. 5: Ultimate internal forces of a double-Ieaf structure with fixed or without leafbond

(8)

The load-bearing capacity then follows from the ultimate limit strain states of the bond cross-section. These are defined by e = eu on the compression edge. On the tension edge, unlimited gaping ofthe joint is admitted. The ultimate internal forces of the structure are calculated by integrating the stress-states which belong to the ultimate \imit strain states. These are represented in the form of interaction \ines of bending moment and normal force. Fig. 5 shows the interaction lines for an unsymmetrical, double-Ieaf structure. The continuous line represents the load­bearing capacity of the bond-section (fixed leaf bond), the broken line represents the load-bearing capacity without leafbond.

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9. LOAD-BEARING CAPACITY OF COHESIVE STRUCTURES WITH MOVEABLE LEAF BOND

If the shear strength 'tu according to eq. 6 is smaIler than 'tlh, the failure moment Mu calculated for fixed leaf bond has to be reduced. For an anaIyticaI solution of the load­bearing capacity of a cohesive structure with moveable leaf bond, the conditions of equilibrium and of compatibility have to be met. For this, the relation between bond stress and movement of the leaf bond has to be known. In most cases it is not known and, furthermore, cannot be sounded at the building in questiono

The simplified ascertairunent relies on the knowledge of the ultimate internaI forces, given a fixed and no leaf bond. The failure moment M..,wb (without leaf bond) does not require any shear stress in the masonry leaf joint, the failure moment hl...fl, requires the shear stress according to eq. 7. For a moveable leaf bond, the failure moment M...mb is interpolated linearly between M..,wb and Mu,fb using the shear strength.

N -- fixed leaf bond

_ .- without leaf bond

Mu.mb Nu~----------~~------~--~

I Mo fb I . I I I

......... I

M

1: fb ~---------------------------"

T L-____________________________ ~

Fig. 6: Failure moment as a function of shear stress

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(9)

10. LOAD-BEARING CAPACITY OF NON-COHESlVE STRUCTURES

Given multiple-Ieaf structures with non-cohesive centre masoruy leaf, the centre leaf does not contribute to the externai load bearing. In anaIogy to the silo model [10], the centre masoruy leaf puts pressure on the externaI leaf both horizontaIly and verticaIly.

The load-bearing capacity under compression and bending is investigated for the externaI leaves onIy, the centre masonry leaf and any leaf bond is not taken into account. The load-bearing capacity is reduced by compressive forces and bending moments originating from the load diversion of the centre leaf (fig 7) as . weIl as by the slenderness of the externai leaves.

. . '

". ' . . '

Fig. 7: Load diversion of a non-cohesive centre masoruy leaf

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11 . REFERENCES

1. Wamecke, P., "Tragverhalten und Konsolidierung von historischem Naturstein­mauerwerk", Dissertation, TU Braunschweig, 1995.

2. Hilsdorf, H.-K., "Investigation into the Failure Mechanism of Brick Masonry Loaded in Axial Compn:;;sion", International Conference on Masonry Structural Systems, Texas, 1968.

3. Probst, P. , "Ein Beitrag zum Bruchmechanismus von zentrisch gedrucktem Mauerwerk," Dissertation, TU München, 1981.

4. Ohler, A., "Zur Berechnung der Druckfestigkeit von Mauerwerk unter Beruck­sichtigung der mehrachsigen Spannungszustãnde in Stein und Mortel," Bautechnik, 5/1986, Veriag Ernst und Sohn, S. 163-169.

5. Mann, W., "Zum Tragverhalten von Mauerwerk aus Natursteinen," Mauer­werk-Kalender 1983, Veriag Ernst und Sohn, S. 675-685.

6. Bemdt, E ., "Zur Druck- und Schubfestigkeit von Mauerwerk - experimentell nachgewiesen an Strukturen aus Elbesandstein, Bautechnik 73, 1996, Heft 4, S. 222-234.

7. Poschel, G., Sabha, A. , "Ein theoretisches Modell zum Tragverhalten von Elbsandsteinmauerwerk," Erhalten historisch bedeutsamer Bauwerke, Jahrbuch 1993, Veriag Emst und Sohn, S .111-118.

8. Ebner, B. , "Das Tragverhalten von mehrschaligem Bruchsteinmauerwerk im regelmãJ3igen Schichtenverband," Dissertation, TU Berlin, 1996.

9. Wamecke, P ., Rostásy, F.S., Budelmann, H. , "Tragverhalten und Konsolidierung von Wãnden und Stützen aus historischem Natursteinmauerwerk," Mauerwerk­Kalender 1995, Verlag Ernst und Sohn, S.623-660.

10. Timm, G., Windels, R., "Silos," Beton-Kalender 1994, SA09-448 .

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