INTERACTION CF MASONRY WALLS ANO CONCRETE SLABS OUE TO LOAOS ANO RESTRAINTS

Salim AI Bosta1)

1. ABSTRACT

This paper deals with cracking of masonry walls and crack opening at the inter­face between reinforced concrete slabs and supporting masonry walls.

At the interface between the slabs and the supporting masonry wall normally a crack develops. The opening of this crack is due to the rotational incompatabi­lity of the concrete slab and masonry. The slenderness of the slab controls its deflection and its rotations at the supports and thereby strongly effects the crack opening. The paper shows, how, for a given permissable crack width , the appropriate slenderness of the reinforced concrete slabs can be derived.

Differential elongations between a roof slab and the exterior walls supporting it, or between roof slabs and lower floor slabs can cause cracking of the masonry walls . The aim of this investigation is to minimize the differential elongation and thereby the tension and shear stresses in the exterior walls.

Recommendations for the design of such types of structures are presented.

Keywords: Masonry Walls, Restraint Stresses, Interaction, Cracks

1) Dipl.-Ing.; Research Associate at the Institute for Structural Design, University of Stuttgart, Germany

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2. INTRODUCTION

Stress and strain resulting from dead and live loads are normally satisfactorily accounted for in structural engineering through structural analysis. There are,

however, many other types of deformation with restraint stresses (temperature, shlinkage, creep, ground deformation, etc.) that are not satisfactorily accoun­ted for. The effects of these deformations can impair the serviceability and dura­bility of the building.

Restraint stresses are brought about through deformation hinderances, which cause cracks after exceeding material's strength limit. The extent to which a crack is harmful depends on its position, size and effects.

3. SLENDERNESS OF REINFORCED CONCRETE SLABS

The deftection of a reinforced concrete (r.c.) slab is composed of elastic deflec­tion under dead and live loads and plastic deflection through creep and shrin­kage in the concrete.

Due to the poor adhesion strength of the bonding area between exterior ma­sonry walls and r.c. roof slabs, the rotation in the end supports cannot be coun­teracted (Fig. 1). A small moment is sufficient to exceed the tensile strength of masonry and generate a horizontal crack underneath the slab support on the externai face of the wall. This deformation can lead to damage; in particular to penetration of water into the wall and flaking of plaster. By limiting the r.c. slab's slenderness, deformation and the resulting damage could be reduced.

hw

-j- t ~<Pw

Figure1 : Deformations at the connection of exterior wall and roof slab

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In the German standard DIN 1045 [1], the slenderness of part of the concrete

elements is limited as span/depth ratio li / d ::; 35 and for floar slabs carrying

partition walls Ij/d::; 150/li (li and h in m, Fig. 2). The permissible deflectian for

general cases is limited by max. f ::; 1/250 and in cases where subsequent da­

mage is expected by max. f ::; 1/500 .

Eurocode 2 [2] regulates the deftection by limiting the slenderness depending

on the load magnitude as in Figure 2; highly stressed !l = Asdb.d ~ 1.5%

and lightly stressed !l = Asdb.d ::; 0.5% (11 = reinforcing ratia, Asl = area af steel, b,d= sectional size).

li = 1.0 I .6- :a..

li = 0.81 .6- I

I I li = 0.61 ..r--- ---+

35 30 25 20

15

DIN 1045 Flat slabs -------, " 4

-~-~Õ.5%--~'~-------~-~-- 1 --------~------~-_. _ _~ _ __~ª- EC 2

---~ 11 ~ 1.5%

2 4 6 8 10

Figure 2 : Slenderness values according to DIN 1045 and EC 2

1

2

3

4

The values in Eurocode 2 lead to considerable larger slab thicknesses compa­red to the values from DIN 1045 . For this reason Eurocode 2 values are re­cammended here for crack control.

4. OEFORMATION OF R. C. ROOFS ANO EXTERIOR MASONRY WALLS AT SUPPORTS

Deflections and elongations arise in a roof slab and the underneath walls and flaar slabs. They are influenced by externai effects; such as laads (snaw, dead and live load) , temperature and moisture. They are influenced also by the pro­perties of the materiais like elasticity modulus, thermal expansion, creep and shrinkage resp. swelling.

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Restraint stresses in the supports of the roof are expected if the changes in the length of masonry wall are incompatible with the r.c. roof slab. This is always the case with the different building materiais and also externai influences, such as different temperatures or moisture contents of the building elements.

4.1 BENDING DEFORMATIONS

The bending deformations of roof slabs arise through loads, creep, shrinkage and also through unequal warming up or cooling down.

Immediately after removing the formwork of the slab, elastic deflection occurs. Through this, rotation of the end tangents of the roof slab will arise at the sup­ports (Fig. 1). The slab's line of support moves towards the inside edge of the wall. Edge stresses are applied to the wall, which result in bending and longitu­dinal deformations of masonry.

The tollowing calculations of the angle of rotation at the support should serve as a model for the evaluation of deformations during service conditions at the connection between externai masonry walls and roof slabs.

First, the angle of rotation <PD is determined (Fig. 1). The eccentricity of the slab support is taken as e = 1/3 d. From here, the twisting angle at the wall heading <Pw is calculated. If the angles are equal, no cracks or subsequent damage are, theoretically, expected. As will be shown, a crack at the contact joint is always expected.

The rotation </JI (</JIO and </JIw in Fig.1) in the serviceability limit state depends on the support conditions of the slab and the externai wall and on the type of loa­ding:

where: k = system and load factor, I = length,

M = max. bending moment, E I = bending stiffness

(1 )

In the cracked state the influence of creep and cracking of the r.c. slab may be considered in the bending stiffness of the slab or by the facto r k". The rotation </JII (</JI~ and </JI~ ) is:

(2)

The width of the crack is found geometrically trom Figure 1:

max w=(</Jo - </JwJ • hw/2 (3)

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The upper limit of the crack width (max. w) is chosen following DIN 1045 [1]

(max. w ~ 0.25-0.40) mm and Eurocode 2 [2] (max. w ~ 0.3 mm) both for

concrete structures. This value (max. w !f 0.3 mm) does not affect the aesthe­tics of the building and its durability.

Roof slabs spanning in two directions are particularly criticai for crack build­up. When there is no load on top, the corners of these slabs lift up .

An accurate calculation of the rotation at the supports for r.c. slabs is very so­phisticated, because of the multitude of different parameters like creep, shrin­kage, crack formation , etc. In the case of masonry, these parameters vary a lot more than in the case of r.c. Above ali , the quality of the masonry work plays the most important role.

Damaging cracks between the slabs and the externai walls can be avoided by keeping within the slenderness limits. With a roof slab slenderness of li / d>25, crack formation has to be reckoned with . Supports should therefore be detailed in such a way that, through suitable measures (s. chapter 5) rotation without construction restraint becomes possible .

4.2 ELONGATIONS

The horizontal elongations of r.c. slabs and supporting masonry walls are diffe­rent due to their different material properties and due to different actions. A stiff connection is created by directly concreting the slab on the externai wall. In such cases restraint stresses will frequently exceed the material strength of the masonry.

For rapid temperature changes and shrinkage the expansions in the wall are checked against masonry ultimate tensil strain . Since the masonry is exposed to stress for a relatively short period of time, the effects of creep and relaxation are of minor importance.

Differences between the horizontal elongations of the two top floors are caused mostly by shrinkage and by different temperatures. One significant parameter of the roof slab's expansion is the temperature at manufacture.

Pfefferkorn dealt with this subject in a clear way [3 and 4]. The principies elabo­rated there, will be drawn up in the calculations to follow.

The roof slab extensions which are at right angle to the wall 's plane usually do not cause cracks, because of the low bending stiffness of masonry walls.

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4.2.1 OIFFERENT OEFORMATION BEHAVIOUR OF ROOF SLABS ANO UNOERNEATH FLOOR SLABS

With the assumption that the softness of masonry provides hardly any restraint compared to massive r. c. slabs, the angle of displacement y (Fig. 3) is calcula­ted as a limiting value trom the difterences of unrestrained expansion of the slabs. In order to avoid damaging crack formation due to shear forces T, the following value of y should not be exceeded [3 and 4]:

where ÓD = expansion difterence between slabs êOo / êDu = upper/lower slab expansion I = criticallength (Fig. 3), H = height of wall

+

r.c. roof slab ~ +=--.=-..e=- r:: - - r ~ =i--~ ~~----+ -=i.~-I I T = s~ear forces ,,--r

\1"- y I I "" II Y

\1 masonry lvall I Ii L ____ J __ J ____________ L

---------------------1 : : r.c. slab I I I I I I I

I I I I L ____ J __ J ____________ L I-----I~-I-----------I

I I Stlft I I I I corei I I _l __ ~_ ~

Figure 3: Elongation of roof slab

(4)

When the masonry shear strength is low, then there is a danger that a horizon­tal crack will form in the first or second longitudinal masonry bed joint under the slabs (chapter 4.2.2 , Fig. 5b) . This crack can be overlapped with the ben­ding crack trom the slab deflection.

4.2.2 OIFFERENT OEFORMATION BEHAVIOUR OF SLABS ANO WALLS

Difterential deformational behaviour occurs when the concrete slabs above and underneath the walls deform relative to the walls due to concrete shrinkage or temperature changes. Similar relative deformation can result trom a change in

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the length of the wall itself. Horizontal shearing forces are produced in the con­tact joints between the wall and slabs which add up in the wall and create hori­zontal stresses (Fig . 4) . In the masonry wall the tensile or shear stress easily exceeds the material strength and cracks will formo

When determining the resulting elongations in the wall and the supports, the temperature changes and the elongations due to shrinkage are assumed to be constant across the entire cross-section of the wall. This causes restraint in the wall, which will be examined in the central cross-section (no bending).

LB--f- L -L -<·~14"-- Lo ~ 1 ,5·H -2 D

T H

1 ~I"~---------L------------------~·I

Figure 4: Horizontal normal stresses and shear stresses in a wall

Figure 4 shows the horizontal stresses and the resulting forces due to tempera­ture changes (here: cooling down in the wall) and shrinkage in a restrained wall. If the normal stress 0x exceeds the tensile strength of the masonry or if the shear stress Lxy exceeds the wall resistance against shearing, a crack forms. According to this there are two different types of wall failure (case A and B):

Case A: The tensile stresses of the wall exceed the tensile strength of the masonry

In this case the resistance of masonry under longitudinal tensile stress (Ro) in the vertical section is smaller than the resistance against shearing (R,) at the horizontal edges; Eq . (5). This occurs for example with an stiff connection bet­ween wall and slab and if the shear stresses do not exceed the wall resistance Rc; Eq. (6) . With an increasing length of the wall section, there is a greater risk of cracks occuring.

If there is an opening in the wall, e.g. a window or a door, then this is an area of particular crack risk. Considering continuous wall regions without openings or other weakenings, the most likely area for cracks to form is the center region ofthe walllength, resp. the B-region (B for beam or Bernoulli [6], La in Fig. 4), where Bernoulli's hypothesis of plane strain distribution applies. Since here the

419

max. horizontal stresses occur due to the greatest deformation hindrances. A crack develops when the tensile stress in the wall exceeds the resistance of material tension (Ro); Eq. (7).

Ra:5 2 Rr (to be more precise: Ra:5 Rrabove + Rrbe/ow )

Fr = d f Lo 'rxy dx :5 Rr = d f Lo (c + Jl . ay) dx

H

Fa = d fax dy ?: Ra

where Ro = resistance of masonry under longitudinal tensile stress R,; = resistance of masonry against shearing F o = resulting tensile force of the wall in the center F,; = resulting shear force of the wall at the upper resp. lower edges

(5)

(6)

(7)

The maximum stress in the uncracked state with complete restraint of thermal extension and shrinkage (~T negativ when cooling) is as follows:

Ox = (- aT . ~T + és) . E

where aT = thermal expansion value of masonry wall ~ T = temperature change in the masonry wall éS = shrinkage value of masonry wall

(8)

Two types of crack can be distinguished (Fig. 5a) crack-type no. 1: failure in the stone and crack-type no. 2: failure in the bed joint. In addition diagonal cracks may develop due to the inclined principie tensile stresses, starting at the upper or lower wall edge (Fig. 5a) crack-type no. 3: failure in the bed joint and crack-type no. 4 : failure in the stone. The longer the wall section, the greater the risk of crack formation. When an initial crack forms, the wall splits in two parts; the middle of which becomes the next area of crack-formation risk, and so on.

Masonry usually absorbs the evenly distributed compression stresses in the wall resulting from increasing temperatures without any problems. Inducing the shear forces from the slabs leads to vertical tensile stresses in the wall are a near the vertical edges. This exposes the masonry to tensile stress vertical to the bed joint. Fig . 5b shows the crack no. 5 caused by this tension. In most cases vertical loads are sufficient to compensate the vertical tensile stresses. The uppermost levei experiences the greatest risk due to the smallloads.

Crack behaviour is predominantly determined by the tensi le strength, degree of

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restraint of the wall, elasticity modulus, wall size, shrinkage and temperature strains.

-.J ...lJ 3 I ~ .1l

~~ i

_I I

1 Fo .L!.- I i

I .L I L

I? F. ...L

l 2' I ;

a) Load case: Cooling down

I \ 6 I \ I , ..... Fo I \ I

J5 I \ i7h-R.~ 1 \

I-F'" ...I. \ 11- • 8 I I

b) Load case: Warming up

Figure 5: Cracks in Exterior Walls due to Restraint Stresses

Case B: Shear stresses at the wall edges lead to slippingl

In this case the resistances R. at the horizontal edges are smaller than the re­sistance Ra in the wall; Eq. (9). Cohesion and friction are overcome by the shear stress; Eq. (10).

2R, :5 Ra (9)

R, = f (e + Jl ay) dx (10)

The wall shifts in comparison to the slabs. The course of the crack primarily de­pends on the bond between stones and mortar and therefore on the workman­ship.The cracks are caused by shear failure mainly horizontally (cracks no. 6 to 8 in Fig. 5 b) in the bed joint, directly at the connection to the slabs or in the bed joint one stone-Iayer below. Thus the horizontal forces F, are induced into the wall at the upper and lower edges along greater lengths than in case A

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(above) , therefore the mean shear stress decreases. After overcoming the co­hesion, only the friction resistance R't is eftective during the slipping of the wall , according to Eq. (11) :

R~ = !(/-l . ay)dX (11 )

In addition to the slipping, deflection of the slabs leads to the support line lifting trom the wall and thus to horizontal cracks in the masonry beneath the slab as shown in chapter 4.1 .

5. PRECAUTIONS FOR AVOIDING DAMAGING CRACKS

The damaging eftects of cracks due to diftering roof slab and masonry de­formations can be avoided by the following items:

- choice of suitable materiais, material combinations, and compatible static systems

- limiting the deformation difterences between the various parts of the building - careful and speedy construction with sufticient time for stripping and curing

of the slabs, depending on the weather - plastering as late as possible - using reinforced masonry work - construction masonry partitions as late as possible - structural detailing to ensure the freedom of movement of structural

elements Iike: slip bearings and separation sheets for the reinforced concrete slabs expansion joints in the externai walls and slabs thermal insulation for the externai walls and roof slabs

6. REFERENCES

[11 DIN 1045: Reinforced Concrete Structures; design and construction , Beuth Verl., Berlin Juli 1988

[21 EC 2, Eurocode Nr 2: Design of Concrete Structures, Part 1, General Rules and Rules for Buildings. CEC, December 1989

[3] Pfefterkorn, w.: Dachdecken und Mauerwerk, R. M. Verlag., Kõln 1980

[41 DIN 18530, Solid slab constructions for roofs; design and workmanship, Beuth Verlag , Berlin Marz 1987

[5] Mann , w.: Grundlagen für die ingenieurmaf3ige Bemessung von Mauerwerk nach DIN 1053 T2, Mauerwerksk.1992, E& S.Verlag, Berlin, 1992

[6] Schlaich, J. ; Schãfer, K. & Jennewein, M.: Toward a Consistent Design of Structural Concrete, PCI Journal May/Juni 1987, vol. 32, no. 3

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