1067

INFLUENCE OF VISCOUS PHENOMENA ON THE BEHAVIOUR OF REINFORCED MASONRY

ANTONIO LA TEGOLA LUCIANO OMBRES Department of Structures, University of Calabria

87036 Arcavacata di Rende - Cosenza (ITALIA)

ABSTRACT

Taking account of the evolution of the state of tension and deformation produced by long-term processes in prefabricated wall panels made of hollow blocks with vertical strengthening, assembled on site in one complete action, we evaluate the short-term processes which cause the collapse of such panels.

INTRODUCTION

In the field of masonry construction, above all for that sei­smic zones, the use of reinforced masonry, made possible by the availability of suitable strengthening (whether vertical or horizontal) is increasingly widespread. Metallic strengthening must be used, both to render the ma­sonry absorbent to typical seismic shock and to obtain the highest resistant quality.

This lather kind of structure is typical of seismoresi­stant constructions constituted from load-bearing and bracing walls, erected on site with the aid of prefabricat~d elements (units), assembled on site and reinforced with suitable stren­gthening steel bars.

One particular type, very common in reinforced masonry, is that in which the unit consists of prefabricated hollow blocks with interior vertical strengthening distributed throu­ghout, the whole assembled on site in one complete processo

Since the structural elements consti tuting such masonry

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are made at different times and with different kinds of mate­riaIs, the global behaviour is influenced by the evolution of viscous phenomena which modify in time the state of ten­sion and deformation produced by long-term processes.

The intervention of short-term processes during the evolution or at the exhaustion of the viscous phenomena, in combination with the long-term actions, can generate a state of tension and deformation corresponding to a final limiting state. It is, however, necessary to identify the mechanism of collapse of the panel and the final values of the short -term actions which caused it.

In the present work we examine the behaviour of a rein ­forced masonry panel placed under a perpendicular centred stress which remains constant with time. The influence of viscosity on the state of tension and deformation of the panel is evaluated, and thereby we determine, as a function of the iJ;lstant of application, the final values of an action of short duration consisting of a horizontal force applied to the top of the panel.

This research is carried out both for the case of panels in which the "uni t" and completion process both use the same kind of materiaIs and are therefore characterized by analogous v iscous cores even if constructed at different times, and for the case of panels made of different kinds of materiaIs, some of which have no viscosity.

MASONRY PANEL SUBJECTED TO ACTION OF LONG-TERM

With reference to fig.1, in the case of a masonry panel sub­jected to a constant, evenly-distributed force,

H -t

N

hj ...,

@un;t _11 ,,'r'< JI~ oI J ,~_. ~.<" .. ~ .. ~ ', ~: ;:~:~ .. ::. nl n1

\\\\'4A"VUA\\'vif', .. ' H= nu' hj nu=number 01 units

Figure 1. '

--

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at the general time t, also in the theory of are:

equa tions which the preservation

govern the problem of plane sections,

N(t) N1 (t) + N 2 (t) + N s ( t )

E:2 (t)

E:3 (t)

constant.

( 1 )

In (1), the subscripts 1,2 and s relate to the material~ which constitute the unit, the completion process and the me­tallic reinforcement respectively.

According to linear viscosity theory, if <1>1 (t,T), <l>2(t,T) represent the functions which express the viscous deformation of materiais at time t, the result is

E: 1 (t) E: e1 (t) + J~ E: e1 (T)<I>l (t,T) dT

E: 2 (t) E: e2 (t) + f t E: e2 (T)<I>2 (t,T) dT (2 )

to E: s (t) E:es(t)

where E:e 1(t), E: e2 (t) and E: es (t) are the instantaneous deforma­tions of the materiais.

According to linear-elast ic constitutive law theory for steel, from (1) and (2) the tollowing system of equations can be obtained:

E: e1 (t) + ft <1>1 (t,T) E: e1 (T) dT E: e2 (t) + J ~e2 (T)$2(t,T) dT to to (3)

E: e2 (t) + lt <I> (t,T) E: e2 (T) dT = N-N1(t)-N2(t)

t 2 Es As o

whose solution enables us to define, knowing the constitutive la.ws of materiais 1 and 2, the state of tension and deforma­tion in the panel as a function of time. If the material constituting the "unit" is not affected by viscous phenomena , we have $l (t,T) = O and (3) becomes:

E: e2 (t) + J t E: e2 (T) <1>2 (t,T) dT to N-N1 (t)-N2 (t)

Es As

(4 )

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Panels made with units and a completion process involving concrete. In this case, us ing the iatter theories of constitutive iaw for a concrete of paraboiic-rectanguiar type and of viscous deformation represented by a core derived from WHITNEY, we can obtain from (3) the foll owing adimensionai reiationships for the va rious possible situations which hold true at the instant to of appiication of the externai force:

a) Eel (to) < Eck E e2 (to) < ECk

ÀCl (t) E; 1 (t) { E; 2 ~ t) Àc 2 ( t) + 2 [ ( 1 -E; 2 (t) ) <p 2 (t ) - ( 1 -t; 1 ( t) ) <h ( t) ]}

(5 )

Àc2 (t)

ECk 2t; 1 (t) E; z ( t) [ ( 1 -E; 1 (t) ) <p 1 (t) - ( 1 -t; z (t) ) <p z (t) -~ Ps ( 1 - t; 2( t) ) <p 2 (t) ]

E [t;l (t) + elPs + + pkE;z(t)]

b) Ee1(to ) < Eck Ee 2 (to) > Eck

In concrete 2, at the instant to, piastification re­suits and it is therefore no longer able to undergo increases in tensioni it cou l d instead experience a partial coiiapse and eventual reloading. Supposing that the coiiapse (ar discharge of ioad) and the reloading follow a rectiiinear course parai iei to the tangent at the origin of the paraboiic iine of the constitutive iaw, we obtain:

ÀCj (t)

Àcz(t)

- Àcz(t) k[n2PS+p] - ÀC2 (t) k nZpZ<p2(t)

2kz2ECk(1-E;l(t))<Pl(t)-ÀC2(t)<P2(t) [Eckkzln2Ps-2t;l(t)]

[2t;1(t) + k 21 ECk(nZps+p)]

C)Eel (to) >Eck Eez ( to) < Eck

ÀCj (t)

Àcz (t)

Eck -Àcz(t) [2t;2(t) e1Ps+ kp] - Ecke lPS(1-t;2(t))<PZ(t)

2E;z(t)ÀCl(t)<Pl(t)-2t;2(t)kllEck(1-t;z(t))(1+nlPS)<PZ(t)

k[2pt;2(t) + k 1Z Eck(1+n1Ps)]

d) Eel(to ) > Eck Eez(to) > Eck

(6 )

(7)

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ÀC1(t)k22~1(t) - Àc2 (t)[k11 + k21n2PS]~2(t)

k 11 + k 21 (n2PS+p)

(8 )

Panels made with brick " un its" and a completion process invol­ving concrete. A consi tutive law of bri ttle linear-elastic type is adopted for the brick and the following relationships are obtained:

ÀCl (t)

ÀC2 (t)

21; 2 (t) sck (1-1;2 (t) )~2 (t) [kll +8 1 ps ]

k[Sck(8 1Ps+k11 ) + 2pI;2(t)]

(9 )

( 1 O)

The variation of tension in the steel in the two cases exami­ned is expressed by the r elationships:

In the (6), (7), (8), (9), (10), (11), is placed:

1 =-- d

dt OC1(t) ÀC2 (t) d dt °C2(t)

k 11 EC1/R~1

n 1

ql

Es/ECl n 2

* * AC1RC1/ASRS

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* k 12 EC1/Rc2 * k 21 EC2/RCl

Es/EC2 nc EC2/ECl

* * q2 Ac 2RC 2 / ASRS

k 22 * EC2 /Rc2

MASONRY PANELS SUBJECTEO TO A COMBINATION OF SHORT ANO LONG-TERM ACTIONS

At the instant tk during the evolution of the viscous phenomenon, besides short and long-term actions the panel is subj ected to those which produce a tensional and deformative state, which, added to the existing one, can correspond to that which characterises the final limiting state of the pa­nel. By identifyng the mechanisms of collapse of the panel it is possible to determine, as a function of tk, the final va lue of the short-term action which has produced the aforementioned limiting state.

With reference to the ted in their aim plane by and by a horizontal force

case of thin masonry panels affec­a constant perpendicular force (N) (P) appli ed to their top, the pre-

valent mechanism of collapse due to normal tension gives way to a mechanism of collapse caused by tangential tensions. The rupture manifests itself through mechanisms of collapse of an

flexural type characterised by the attainment of maximum deformation in the section most under stress.

p ----. lN

h

~<;,;wA~''<?M'7k~''''V-7~

Figure 2.

Still according to the hypothesis of the validity of the principle of preservation of p lane sections, i t is possible to identify the t wo mechanism illustrated below:

-

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a) Collapse due to attainment of final deformation in the ma­terial constituting the "unit":

H +

Figure 3.

Eo(t k ) = deformation at the instant t k produced by long-term action. In this case the following limitations apply:

b) collapse due to the attainment of final deformation in the stretched steel . In this case the following situations hold true at the same time:

I H

~

[j lli1 ~';."" \/! :~~~

~ ~.,

",'0;-

:;:j;' \':~.

~

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j. Co { t k)

(1)T Xc 1

+

Figure 4.

+ 81 (t k )

Xc

C1max I ~

In the two mechanisms, the diagram of deformation produced by short-term a c tion is completely defined when x ~ l) is known.

The value of xá ll is determined through the equilibrium condition at the translation L'l N O; the final moment of the section M is determined from the known xP) of the rota ­tional equilibrium condition, and from the consequence of having Mu = P H we can determine the value of the short-term action P which is associated with it.

In the case of a panel under stress at right angles to its own plane, the analysis of the state of deformation and tension produced by the combination of short and long-te r m actions is accomplished by making ref e rence to the singl e " unit".

NUMERICAL APPLICATIONS

Wi th reference to the cases of reinforced masonry made with concrete ("unit" and completion process) and with concre­te and brick, numerical applications have been conducte d which have enabled us to define the variation of the tensional state in the materiais and of the final value of the short and long-term action over a period of time, for different va­lues of long-term actions and of the geometrical and mechani­cal parameters which characterise the problem being studied.

Some of the results of such applications are presented in the figures 5, 6 and in the table 1.

-

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~ ~ ~ (\ _o,02P

Ih d N = 800 t --'

/ ~ p--~~ H ~ 240 em

/ ;...--" h = 600 em

~ t:=--~ ~ V I

so.OO~ ! ~ k= 0.714

- 0.016 º= 2.57 p"'/'

140

120 V-/ Q= 0.020

fYk = 3800 kg/em 2

~ (>s 0.00 80 s -v.v o

ºs 0.D20

40

o 2 4 6 8 10 12 14 16 18 20 t (mont hs)

F igure 5. Panels made with units and a complete process invol­ving c oncrete . o (t) versus -t( <p 2 (t) =2<h (t)) [ . Os (t) / 20; * 0c 2 (t) ;.oc 1 (t) 1

~

hIú )

N = 500 t * O lO.009 O H=240 em

h=600em ~ ~:: 0.016 O ~

-On?O

k = 0.714 ""5

18

16

140 º = 2.57

12 O fyk = 3800 kg /em 2

80

i--4 - ..-- -=--=-f--=-_ O

~- I- --r_-.u--- .=--=- -- I-- - - --:;::::.-::: -- - ....

,.-,~

10

~ ~. -. ..;;; ::-~.~ -:::.,-:-~~ ...:.:-=., =:='. -= -. '-. ;::". -:= ::!.. r-' - -'- ~c=::: ::=-: :-=.:...-:-

O

60

40

20

O 2 4 6 8 10 12 14 16 18 20

Figure 6. Panels made with brick "units" and a completion pro­cess involv ing concrete. [--- 0s (t)/20; - 0brick(t); - -- --oc (t) 1

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TABLE Varia tion of the final value of short-term action P(t) [Kg]

Os t m::mths

o 1 2 3 4 5 7 9 11 13 o 0 . 009 12636 18654 12669 12686 12698 12711 12731 12748 12761 12772 ON

~ o 0.016 15830 16079 16125 16168 16210 1625 1 1632 5 16362 16382 16404 " "-"5,~ 0 . 020 17702 17717 17727 17744 17762 17774 17806 17905 17987 18037 ...

o 0 . 009 10996 10988 10981 10974 1 0966 10961 10954 ON ~ o 0 . 016 13888 13967 14853 14900 14939 14985 15072 15146 15215 " "--'< ry ><~ 0.020 16550 16590 16625 16662 16695 16728 16787 16845 16889 1 6935 ...

CONCLUSIONS

The numerical applications have shown that in general , the inf luence of the viscous phenomena brings about an improve­men t in the capacity of the panels to withstand short-term actions applied in the plane at right angles to that of th e panel. This improvement is much greather when the percentage ofmetal lic reinforcement is increased.

On the other hand, the phenomenon is different in the ca­se of masonry constructed wi th brick and concrete: in such a case i t is possible to verify the collapse of the panels due to brittle rupture.

REFERENCES

1. La Tegola, A., Gli effetti della viscosità nelle sezioni in cemento armato. Ingegneri, 1965.

2. Migliacci, A., Applicazioni dei principi di viscos ità, Qua­derni del Corso di Perfezionamento per le costruzioni in c.a .. Fondazione F.lli Pesenti, Tamburini Editore, Milano, 1971 .

3. Mikluchin, res, The Sistems. Austin.

P.T., Rheological behaviour of masonry structu ­International Conference on Masonry Structural

College óf Engineering, University of Texas at

4. Turnsek, V. and Cacovic, F., Some experimental results on the strength of brick masonry walls, Proceedings, 2 Inter­national Brick Masonry Conference, Stoke-on-Trent, 1970.

5 . Benedetti, D. and Tomasevic, M., Sulla verifica sismica di costruzioni in muratura, Ingegneria Sismica, Giugno 1984.

6. Del Piero, G., Le costruzioni in muratura, CISM Udine.