BUILDING RESEARCH JOURNAL

VOLUME 55, 2007 NUMBER 3

Hysteresis analysis of prestressed brick frame with strawbale

masonry-infill subjected to seismic loads

A A Adedeji

Department of Civil Engineering, University of Ilorin, Ilorin, Nigeria

Email: amadeji@yahoo.com

Pseudo-dynamic earthquake response tests, of a one quarter (¼) scale model

three storeys prestressed bricks frames stiffened with cement plastered

strawbale masonry, was conducted. The structure was idealized as plane

frames. The analysis utilised the hysteresis models for members’ models as

time-independent. The force-displacement relationship of the members’

models was evaluated by the approximate method on the basis of the

material properties and structural geometry. A hysteretic model was

investigated with straw bale infill panel to determine the hysteretic

parameters, stiffness deterioration and strength degradation due to seismic

loadings. The average design thickness, for the cement-plastered strawbale

stiffens the prestressed burnt-brick frame, was obtained.

Keywords: seismic; masonry-infill; strawbale, finite element; degradation,

prestressed brick

1. Introduction

A number of past studies (Klinger and Bertero 1978; Bertero and Brokken 1983; Mander and

Nair 1994) focused on evaluating the experimental behavior of masonry infilled frames to

obtain formulations of limit strength and equivalent stiffness. A more rigorous analysis of

structures with masonry infilled frames requires an analytical model of the force –

deformation response of masonry infill. While a number of finite element models have been

developed to predict the response of infilled frames (Dhanasekar and Page 1986. Mosalam

1996, Malnotra 2002), such micro modeling is time-consuming for analysis of large

structures. Alternatively, a macro model allows treatment of the entire infill panel as a single

unit.

Saneinejad and Hobbs (1995) developed a method based on the equivalent diagonal strut

approach for the analysis and design of frames with masonry infill walls subjected to in-

plane forces. The UBC required that the shear walls acting independently of the ductile

moment-resisting portions of the frame shall resist total required seismic forces. It is also

required that design force distributions along elevations of the structure for both axial-

150

flexural and shear design shall be the same. It has been observed from the research carried

out by Ahmet et al (1984) the UBC later claim could be realized by shear design based on

calculation that demands that consider actual flexural capacity of the walls. The actual

contribution of the edge members (columns and beams) panel RC/ prestressed concrete

should be considered in evaluating available shear strength. Therefore the study has

recommended that in designing and evaluating of strength of wall, cross section should be

considered rather than the assumption of edge column acting as axially loaded members that

should resist all vertical members from the loads acting on the wall.

Based on the aforementioned claim, the objective of this paper was to provide the

average design thickness for the cement-plastered strawbale stiffens the prestressed burnt-

brick frame. Data on strength and deformation of the structure are the input for the analytical

models. The plastered strawbale wall was connected to the frame with mortar (1:6 cement-

sand mix) to constitute a simple support. This is shown in Fig. 1. The project also covers the

hysteresis analysis of the straw bale wall infill in terms of stiffness deterioration and strength

degradation in order to determine the response of the infill due to dynamic loading.

Prestressed brick beam

B Tendon

A

Bar tie A’

Joint mortar

Strawbale

wall

B’

VERTICAL SECTION SECTION B-B’

Prestressed brick column

HORIZONTAL SECTION A-A’

Fig. 1.Infill-frame interaction

A A Adedeji

151

2. Modelling of Structural Members 2.1 Frame: Beam and Column Members

A one-dimensional model was used for beam and column in this paper. The beam or column

member was idealized as a perfectly idealized elastic massless line element with two

nonlinear rotational springs at he two ends. The model could have two rigid zones outside the

rotational spring.

2.2 Analytical Model of strawbale Infill Shear walls can be idealized as (a) an equivalent column taking flexural and shear

deformation into account, (b) a braced frame in which the shear deformation is represented

by deformation of diagonal elements, where the structural deformation is by the deformation

of vertical element and (c) short line represent along the height with each short segment with

hysteretic characteristics. These models have advantages and disadvantages. In most cases

the horizontal boundary beams are assumed to be rigid.

The proposed analytical model assumes that the contribution of the straw bale wall infill

panel (Fig. 3a) to the response of the infilled frame can be modeled by replacing the panel by

a system of two diagonal straw bale wall compression struts (Fig 3(b)). Since the tensile

strength of masonry is negligible, the individual straw bale strut is considered to be in

effective in tension. However, the combination of both diagonal struts provides a lateral load

resisting mechanism for the opposite lateral directions of loading. The lateral force-

deformation relationship for the structural straw bale infill panel is assumed to be a smooth

curve bounded by a bilinear strength envelope until the yield force Vy and then on a post

yield degraded stiffness until the maximum force Vm is reached (Fig 3). The corresponding

lateral displacement values are denoted as Vy and Um respectively.

2. 2.1 Strawbale Wall as Infill Panel

The use of strawbale infill for the construction of a building in place of conventional

materials is its cheapness, availability and flexibility in terms of workability and strength.

Rigid zone

Elastic element

Non-linear rotational

Springs

Fig. 2. One-dimensional model for beam and column

Hysteresis analysis of prestressed brick frame with strawbale

masonry-infill subjected to seismic loads

152

Though the individual straw bale strut is considered to be in effective in tension, yet

strawbale masonry has a high tensile strength.

The load resisting mechanism of infill frames is idealized as a combination of moment

resisting frame system formed by the frame and a pin-jointed system formed by the

strawbale. However, because of the absence of a realistic, yet simple analytical model, the

plastered straw bales as infill panels might be neglected in the non-linear analysis of building

structures. Such an assumption may lead to substantial inaccuracy in predicting the lateral

stiffness, strength, and ductility of the structure.

Saneinejad and Hobbs (1995) developed a method based on the equivalent diagonal strut

approach for the analysis and design of steel or concrete frames with masonry infill walls

subjected to in-plane forces. The method takes into account the elastoplastic behaviour of

infilled frames considering the limited ductility of infill materials. The formulation provides

only extreme or boundary values for design purposes. In the case of straw bale panel, the

aspect ratio, shear stresses at the interface between the infill and frame, together with the

frame strength were accounted for and the formulation expresses the boundary values for

design purposes.

3. Equivalent Strut Model The description, in brief, of the formulations for predicting the lateral strength and stiffness

parameters of the strawbale infill-panel is presented in this section.

Considering the straw-bale infilled frame as shown in Fig 3 (a) and Fig.4 , the maximum lateral

force Vm and corresponding displacement Um in the infill straw bale panel are expressed as,

Vm+ (Vm

-) < Ad f m cos < Vtl < 0.83tl (1)

(1-0.45 tan ) cos cos

Um+ (Um

-) = mLd (2)

Cos

where t = thickness of the infill panel: l = lateral dimension of the wall panel : f’m =

masonry strength, m = corresponding strain, = inclination of the diagonal strut to the

horizontal; V =

Fig..3 Strength envelopes for masonry infill

K0

Kpy Um- Uy

-

Uy+ Um

+

Vy-

Vm-

V

Vm

Vy

Ko

A A Adedeji

153

V = shear strength (average of 0.347 N/mm2), of straw bale wall; and Ad , Ld = area and

length of the equivalent diagonal struts respectively calculated as,

Ad = (1- c)c t h c + b t l b < 0.5t h f a / fc (3)

c c cos

and

(a) Straw bale wall infill frame sub assemblage

Straw bale

infill panel

h

h

Frame

1

1

(b) Straw bale wall infill panel

Fig. 4. Wall equivalent diagonal strut

(1

-

b)

h

b h

l

h

Hysteresis analysis of prestressed brick frame with strawbale

masonry-infill subjected to seismic loads

154

Ld = ((1 - c )2 h

2 + L

2 (4)

Where the quantities c, b, = ratio of wall length (breadth) to the contact length between the

infill and frame respectively, c, b, compressive and shear stress of wall respectively, a,

and c, compressive strength for frame and wall respectively. Saneinejad and Hobbs (1995)

proposed the formulations of the equivalent strut model. The initial stiffness Ko of the infill

straw bale wall panel is estimated using the following formula.

)5(2

m

m

oU

VK

The lateral yield force Vy and corresponding displacement Uy of the infill panel may be

calculated from geometry as;

)6(1

)(

mom

yy

UKVVV

)7()1(

)(

o

mom

yyK

UKVUU

where = ratio of post yield stiffness (Kpy) to initial (Ko) stiffness (See Fig. 2)

4. Seismic Load Analysis 4.1 Time-independent smooth hysteresis model

A smooth hysteretic model proposed by Beber and wen (1981) is used for the structural

straw bale masonry infill panel. The model, which was developed based on the Bouc–Wen

model for hysteresis behaviour furnishes a smooth hysteresis force-displacement relationship

between force V and displacement U is,

Vi = Vy [i + (1 - ) Zi] (8)

Where = ductility calculated as Ui/Uy, subscript i = instantaneous values, subscript y =

yield values, and Z = hysteretic component determined by solving the following differential

equation by Reinhorn (1995) as;

dZi = [aeff – Zi n [ sgn (di Z) + ]] d (9)

where signum function sgn( x) = 1 for x > 0 and = -1 for x < 0; aeff , , and = constants

that control the shape of the generated hysteretic loops (Assumed values aeff = 1, and = =

0.5. At x = 0, the effect of cyclic loading is neglected) and n controls the rate of transition

from the elastic to yield state.

4.2. Stiffness decay The yielding system in general is the loss of stiffness due to deformation beyond yield

point. The stiffness decay is incorporated directly in the hysteretic model by including the

control parameter in equation (9) for hysteretic parameter Z in which is obtained by

pivotal deterioration method (Valles et al, 1996).

A A Adedeji

155

dZi =[ aeff - Zin[ sgn(diZ)+] ] di/ (10)

)11(]1)1([

ik

ik

S

S

for I > 1.0

where Sk = multiplier for Vs to define the pivot for stiffness deterioration. A default value of

Sk is taken to be 5.

4.3 Strength degradation

Degrading systems such as straw bale wall infill panels will also exhibit loss of strength in

the inelastic range. The strength deterioration is modeled by reducing the yield force Vy from

the original value Vyo at each step k,

Vyk = Vy

k (1 – DI) (12)

in which DI = cumulative damage parameter dependent on the maximum attained

ductility, max, and the cumulative energy dissipated ( Valles 1996).

)13()1(

25.011

12

1max

Sp

cy

p

c

d

V

VSDI

where max, c = maximum and monotonic ductility capacity and parameters Sp1 and Sp2

control the rate of deterioration for maximum and monotonic ductility respectively. The

damage index was derived from fatigue consideration (Reinhorn et al, 1995).

4.4. Cracking slip model

Opening and closing of masonry cracks resulting in the pinching of hysteresis loops is a

commonly observed phenomenon in masonry structural systems subjected to cyclic loading.

The concept of slip lock element proposed by Baber and Noori (1984) was adopted in this

study to formulate a hysteretic model. A slip–lock element is incorporated in series so that

displacement ductility = 1 + 2, with the smooth degrading element 1. The displacement

ductility component 2 due to the slip-lock element is defined by the following relationship:

d2 = a f(Z) dZ (14)

in which a = (As(2-1), at As is the parameter for varying the slip length due to crack opening

in the panel and 2 = ductility attained at the load reversal prior to the current unloading or

reloading cycle.) is the slip length and assumed to be a function of the attained ductility while

the function f(Z) is defined as:

(Z) = exp((Z -Z1 )2) (15)

Zs2

Hysteresis analysis of prestressed brick frame with strawbale

masonry-infill subjected to seismic loads

156

at -1< Z, and Z1 < 1

where Z1 = value of Z at which f(Z) reaches its maximum; Zs = range of Z , about Z = Z1

, in which the slip occurs. Derived from Eq.(9), (14), and (15), the hysteretic parameter Z

will satisfy the following differential equation (Reinhorn. 1995).

)16(

]))sgn(({[)(

exp1

]}).sgn(({[

2

2

ZdZa

Z

ZZa

ZdZa

d

dZ

n

eff

s

n

eff

5. Experimental Tests 5.1 Test Structure and properties of materials The test structure represented a three-storey one-bay (span prestressed concrete ductile

moment resisting frame filled with straw bale masonry), built at a scale of ¼. The overall

geometry of the test structure is depicted in Fig. 5. Analytical example was carried out for a

full scale version of the test structure and all pertinent quantities were scaled using the length

factor of 0.25. Each tested structure consists of strawbale wall (made of 127x78x61 mm3 unit

size; elephant grass bale plastered with 1: 6 cement-sand mix ratio; average density of 2200

kg/m3; 12% absorption and moisture content of 3.61. Its average compressive and flexural

strengths are 2.83 and 1.56 N/mm2) respectively) whose principal plane was parallel with the

direction of the input motion. The prestressed bricks frame (column-beam) was constructed

of concrete with grade of 40 N/mm2

and cable of diametre 12mm.

Column 0.75

Beam

0.75

Mortar

Wall 0.75

SECTION A-A’

0.075

0.05

1.26

0.05

0.075

1.26

0.075 0.05 0.05 0.075

PLAN

All dimensions in m

Fig. 5. Test structure

A A Adedeji

157

Design gravity loads comprised of 70 kN (self weight and live load). Seismic design

effects were determined using modal spectral analysis. The design spectral ordinates were set

so that the first-mode shear base was equal to the design base shear required by the UBC

1982 for a ductile moment-resisting space frame. Also, the response spectrum was selected to

reflect soil condition that superseded by a layer of sandy soil. Earthquake design actions were

determined with a three dimensional elastic analysis model based on the cross section of

columns and beams. The three dimensional structure was idealized as a pseudo-three-

dimensional model in which only the planar modes of the main structural systems (walls and

frames) were considered. The considerations of stiffness and strength of frame elements

perpendicular to the plane of the transverse walls and frames were not considered. Perfect

base fixity of the frames was assumed.

Horizontal floor level responses have been recoded in lateral and main direction.

At 3.2 m/s2, the structure did not increase its response. The maximum base shear of 129

kN is obtained at the roof displacement of 12.3 mm.

5.2 Test and Instrumentation Tests included earthquake simulation of varying intensity and followed by low amplitude

free vibration tests. The simulations were conducted by applying unilateral horizontal base

motions parallel to the direction frame. The input signals to the shaking table modeled

accelerated history for uniaxial tests are as indicated in Table 1 with a total of four

earthquake records. These values were used as input ground motions in the dynamic analysis.

These values are notations used for individual ground motion, the components of earthquake

motion record, peak ground acceleration (aeff) in terms acceleration due to gravity (g), peak

ground velocity (vg), significant duration of the accelerogram (tSD) and the normalized

characteristics intensity (In).

Table 1 Characteristics of selected input earthquake ground motion Ground

motion

Notation Peak

ground

acceleration

(aeff)

Peak

ground

velocity

(vg) m/s

Significant

duration

(tSD), s

normalized

characteristics

intensity (In)

El Centro ELCENT 0.35g 0.34 24 2.66

Haruka-oki HARU 0.42g 0.46 6 2.12

Silmar SYLM 0.84g 0.61 47 1.71

Hacinohe HACH 0.23g 0.34 28 1.52

6. Typical Analysis Example 6.1. Sections properties

Beam and column sectional area are shown in Fig. 6 . Second moment of area (Ib) = 2.278

x 10-3 m

4(Ic) = 6.75 x 10

-4 mm

4 respectively. The straw bale wall is measured acting as

diagonal members of the frame in this analysis. It acts as a stiffening element and the area

Hysteresis analysis of prestressed brick frame with strawbale

masonry-infill subjected to seismic loads

158

and length of the equivalent diagonals are as calculated below, Ld = 6681.6mm and area of

equivalent diagonal strut (Fig. 6)., Ad = 14235.0 mm2.

6.2. Earthquake analysis and loading

For the absorption and dissipation of the energy through its motion, the frame of the

building must be sufficiently ductile. For calculating ductility and other parameters it is

assumed that the tests were entered to the ductile mode. Fig 7 shows the calculated shear

loading during seismic excitation. It is assumed that during a strong ground motion the

inertial of a building results in a horizontal shear force at the base and proportional to the

weight of the building and the imposed ground motion, so that:

VD = Cs M g (23)

And

)24(R

SIaC

nffe

s

where VD = total dynamic base shear, M = total mass of the building and its contents (kg), g

= acceleration due to gravity, Cs = seismic coefficient, aeff = dependent effective peak

acceleration , S = seismic response factor, R = factor related to ductility of structure or force

reduction factor, and In= normalized characteristics intensity. A good example of the seismic

record characteristics is given by Moroni et al (1996) from 1985 Chilean earthquake.

Assumed for the prestressed brick frame is the ductility factor R = 5 (braced frame, with

C

A

B

D E

F

G

H

3 @

3 m

= 9

m

6 m

(a)

Fig..6. A three-storey building

300 mm

450 mm

(c) Column section

300 mm

450 mm

( b) Beam section

Ad

A A Adedeji

159

effective peak acceleration aeff = 0.1 – 0.2g, seismic response factor S = 2 and the intensity

factor = 1, so that the seismic coefficient Cs = 0.04. The total design base shear is 143.3kN.

6.3 Analysis of bare frame

The basic concept of this method is based on the fact hat the inertia of a building result in a

horizontal shearing force at the base proportional to the total weight of the building and to the

imposed ground motion during a period of strong ground motion.

6.4. Database

The three-storey building shown in Fig 8 has been analysed by the equivalent lateral force

procedure. Weight at each storey level = 21.63 x 6 = 129. 8 kN, Weight at the roof = 17.61 x

6 = 105.66 kN and the total mass Mtotal = 36.526 kg. Therefore the total design base shear =

256.4 kN.

The lateral forces on the building are distributed over its height accordingly. The sum of

the lateral forces is equal to the total base shear. The lateral forces on the building frame are

shown in Table 2 and Fig. 8.

Table 2 Seismic forces on Building frame

Storey level Equivalent

lateral force

(kN)

Equivalent

lateral shear

force (kN) Roof

2

1

41.45

71.65

143.3

41.45

113.10

256.40

Total dynamic base shear 256.4

A

B

C

D E

F

G

H

3 @

3.0

m =

9.0

m

6.0 m

17.61 kN/m

21.63 kN/m

21.63 kN/m

Fig.7. Equivalent Lateral Loads

Horizontal

load during

seismic excitation

Horizontal

load during

seismic excitation

Horizontal

level during

seismic excitation

Hysteresis analysis of prestressed brick frame with strawbale

masonry-infill subjected to seismic loads

160

The maximum lateral force and corresponding displacement in the infill straw bale panel

are as follows:

At = 32o and using equations (1) to (7), Vm

+ (Vm

-) = 14486.4N = 14486N, while the

corresponding displacement Um+ (Um

-) = 23.6mm. The initial stiffness Ko of the infill panel is

estimated Ko =1227.63N/mm, the lateral yield force and displacement of the infill panel is

14193 .4 N and Uy +(Uy

-) = 11. 7mm. Using different straw bale thickness, the result of the

analysis for the stiffness deterioration and shear decay are shown in Table 3.

Table 3 Stiffness deterioration and shear decay of straw bale infill for the

thickness (t) = 300m

Instantaneous

value, (i)

Displacement

Ui (mm)

Lateral force

Vi (N)

Shear decay

(Vm - Vi (N)

Initial stiffness

Ko (N/mm) 1

2

3

4

5

6

11.7000

11.8183

11.9169

11.9988

12.3825

23.6000

14340.1

14365.2

14386.2

14403.6

14485.1

14486.4

146.3

121.20

100.2

82.80

1.30

0.00

25.009

20.511

16.817

13.801

0.209

0.000

CASE II, t = 275mm, Ad = 13048.8mm2, Vm = 13279.2N, Um = 23.6mm, KO=1125. 4N/mm,

Vy = 13145.1 N, Uy = 11.7mm.The result of the analysis is shown in Table.2

Fig.8. Members moments and shear

forces

430.16 kN

300.36 kN

158.5

36.21

158.6 158.6

36.21

158.5

A A Adedeji

161

Table 2 Stiffness Deterioration and shear Decay of straw bale infill for the

thickness (t) = 275mm

Instantaneous

value (Test

No) i

Displacement

Ui (mm)

Lateral force

Vi (N)

Shear decay Vm

- Vi (N)

Stiffness initial

Ko (N/mm)

1

2

3

4

5

6

11.7000

11.8179

11.9162

11.9979

12.3803

23.6000

13145.1

13168.1

13187.2

13203.1

13277.6

13279.2

134.10

111.10

92.00

76.10

1.60

0.00

22.923

18.802

15.441

12.686

0.259

0.000

At the instantaneous value 6, other cases (CASES III and IV) with varying wall

thicknesses (t) are:

CASE III at t = 250mm,

Ad = 11862.53mm2, Vm = 12071.9N, Um = 23.6mm, KO=1023. 05N/mm, and Vy = 11949.9

N, Uy = 11.7mm .

CASE IV, t = 200mm,

Ad = 10961.62mm2, Vm = 11155.2N, Um = 23.6mm, KO=945. 36N/mm and Vy = 11042. 5N,

Uy = 11.7mm.

6.5. Deflection check

Maximum deflection of masonry wall is 24 mm. This value is greater than 23.7mm that was

obtained in the analysis. Thus, the maximum deflection of the straw bale infill is less than the

maximum allowed for masonry walls with the same dimensions (6.000 x 3.500 m).

It is beyond the scope of this paper to verify the accuracy of the spectra response on the

basis of the shake table runs and because of the compressed time-scale of the laboratory

study (at Department of Civil Engineering, University of Ilorin), it would not be correct to

make such correlation. However, it is worthy to examine how well the actual peak response

agreed with those determined from the linear response from actual base motion. The results

are shown in Table 4.

Table 4. Observed and measured response maxima for base isolated motion Response Table

acceleration

Peak

acceleration

Spectral

acceleration

Base

shear

kN

Total

weight of

the

structure

kN

Base

moment

kNm

Roof

displacement

Mm

Observed

(prototype)

1.07 0.58 0.59 129 210 95.8 12.3

Calculated - 0.1 - 143 365.62 158.6 23.6

6.6. Dynamic response results

At calculated Z =1, the stiffness decay is incorporated in the hysteretic model by

including the control parameter for the hysteretic parameter (i > 1.0). The default value of

Hysteresis analysis of prestressed brick frame with strawbale

masonry-infill subjected to seismic loads

162

Sk = 5 is recommended. The results of iteration of dynamic response characteristics from the

analysis are as shown in the Tables 5 and 6 for 200 and 250 only.

Table 5 Dynamic response characteristics of straw bale infill thickness (t) = 200mm Displacement

(Ui)

Ductility

(i)

Control

parameter (i)

Hysteretic

Component (dZi)

Lateral force

(Vi), N

Shear decay

(Vm –Vi), N

11.7 1.0 1 1 11042.5 112.70

11.8205 1.0103 0.9983 1.0017 11.062.22 92.98

11.9210 1.0189 0.9969 1.0031 11078.66 76.54

12.0045 1.0260 0.9957 1.0043 11092.32 62.88

12.0737 1.0319 0.9948 1.0053 11103.64 51.56

12.1311 1.0368 0.9940 1.0061 11113 42.20

12.1782 1.0409 0.9933 1.0067 11120.72 34.48

12.2171 1.0442 0.9928 1.0073 11127.09 28.11

12.2491 1.0469 0.9923 1.0077 11132.33 22.87

12.2754 1.0492 0.9920 1.0081 11136.64 18.56

12.971 1.0510 0.9917 1.0084 11140.13 15.03

12.3148 1.0526 0.9914 1.0087 11143.08 12.12

Table 6 Dynamic response characteristics of straw bale infill thickness (t) = 250mm Displacement

(Ui)

Ductility

(i)

Control

parameter (i)

Hysteretic

Component (dZi)

Lateral force

(Vi), N

Shear decay

(Vm-Vi), N

11.7 1 1 1 11949.9 122

11.8224 1.0105 0.9983 1.0017 11971.58 100.32

11.9245 1.0192 0.9968 1.0032 11989.65 82.25

12.0094 1.0264 0.9957 1.0044 12004.67 67.23

12.0797 1.0325 0.9947 1.0054 12017.12 54.78

12.1378 1.0374 0.9939 1.0062 12027.41 44.49

12.1858 1.0415 0.9932 1.0069 12035.9 36.00

12.2253 1.0449 0.9927 1.0074 12042.9 29.00

12.2578 1.0477 0.9922 1.0079 12048.66 23.24

12.2846 1.0500 0.9918 1.0082 12053.4 18.51

12.3066 1.0518 0.9915 1.0086 12057.29 14.62

12.3246 1.0534 0.9913 1.0088 12060.48 11.46

Other dynamic response results for t = 275 and 300 are not shown here, but are represented in

the graphical forms. The strength deterioration is modeled by reducing the yield force Vy

from Vyo at each step k.

7. Results and Discussion

It was observed, from the result of the analysis, that the maximum lateral force the straw

bale infill can be subjected to increases with the thickness of the infill panel. For thickness of

200mm,Vm = 11155.2N; for t = 250mm,Vm = 12071.9N; for t = 275mm, Vm =13279.2N and

for t = 300mm, Vm = 14486N. Also, the stiffness and strength (hysteretic properties) of the

straw bale wall infill decreases after the yield force. The yield force (Vy) being 14193.4N for

t=300mm; 13145.1N for t = 275mm; 11949.9N for t = 250mm and 11042.5N for t = 200mm.

The maximum deflection of the infill was obtained to be 23.7mm, which was less than the

A A Adedeji

163

maximum 24mm specified for masonry infill walls. Also, it was found out that the hysteretic

parameters deteriorate at a rate proportional to the thickness of the infill panel

As a result of the seismic loads, the force-displacement relationships for the loading

cases, stiffness decay and the wall strength degradation are shown in Figs. (9), (10) and (11)

respectively.. The hysteresis-energy dissipation due to seismic load was reduced detriment to

damage of the structure.

It was also observed that the structure shear decay increases with decrease in ductility of

the wall infill.

Fig. 9 Force-displacement relationship for strawbale infill

(at t = 200 to 300mm)

-20000

-10000

0

10000

20000

-20 -10 0 10 20

Deflection U, mm

La

tera

l F

orc

e V

, N t=200mm

t=250mm

t=275mm

t=300mm

Fig. 10 Hysteresis curve with stiffness decay

-30

-20

-10

0

10

20

30

-20 0 20

Deflection (U,mm)

Stiff

ness

Dec

ay (2

(Vm

-

Vi)/

Ui)

N/m

m

t=200mm

t=250mm

t=275mm

t=300mm

Hysteresis analysis of prestressed brick frame with strawbale

masonry-infill subjected to seismic loads

164

Fig. 11. Hysteresis curve with strength degradation

-200

-150

-100

-50

0

50

100

150

200

-20 -10 0 10 20

Deflection U, mm

Sh

ea

r D

eca

y (

Vm

-Vi)

, N

t=200mm

t=250mm

t=275mm

t=300mm

8. Concluding Remarks

The use of straw bale wall as an infill panel for the proposed hysteretic model can compete

effectively with other conventional materials, such as earthwall (Adedeji, 2002), since its

maximum deflection Um, is less than that specified for masonry walls.

Though a perfect base fixity of the frames was assumed, the structure did not increase its

response at 3.2 m/s2. The maximum base shear of 129 kN is obtained at the roof

displacement of 12.3 mm. these are far less values than the analysis results.

The computed force-deformation response can be used to assess the overall structural

damage and its distribution to a sufficient degree of accuracy.

The structural materials characteristics were nominal values and may be different from the

prescribed values. Such characteristics of materials for further analysis should be based on

the confined and unconfined prestressed concrete.

9. References Adedeji, A.A. (2001). Hysteresis analysis of framed structures stiffened with earth wall infill

subjected to seismic Impact, Conference Proc. SUSI–2002, UK.

Adedeji, A.A. (2003). Analytical approach to framed structures stiffened with earth wall

infill subjected to seismic loads, LAUJET Journal, 1(1).

Ahmet, E., Aktan, M., Vitelmo, V and Bertero, E., (1984), Seismic response of R/C frame-

wall structures, Journal of Structural Engineering, 111(8), 1803 – 1821.

Berber, T. T. and Noori, M. N. (1985). Random Vibration of degrading pinching system,

Journal of Engineering Mech, ASCE 11(8): 1011-1026.

Bertero, V.V., and Broken, S. (1983). Infills in Seismic resistant building. Journal of

Structural Engineering., ASCE. 109 (6): 1337-1361.

Bouc, R. (1967). Forced Vibration of Mechanical systems with hysteresis, Proc: 4th

Conf. on

Non- Linear Oscillation.

A A Adedeji

Hysteresis analysis of prestressed brick frame with strawbale

masonry-infill subjected to seismic loads

165

Dhanasekar, M.., and Page, A.W. (1986). The influence of brick masonry infill properties on

behaviour of infilled frames, Proc., Instin. of Civ. Engrs., London England, Part 2. 593-

605

Ibrahim, E.A. (2001). Hysteresis analysis of framed structures, B. Eng. Project, Submitted to

the Dept. of Civil Engineering, University of Ilorin., Ilorin, Nigeria.

Klinger, R.E., and Bertero, V. V (1978). Earthquake resistance of infilled frames, Journal of

Structural Engineering, ASCE.104 (6)

Madan, A., Reinhorn, A.M, Mander, J.B, (1997). Modeling of masonry infill panels for

structural analysis, Journal of Structural Engineering, ASCE 123(10)

Mander, J.B., and Nair, B. (1994). Seismic resistance of brick-infilled steel frames with and

without retrofit, The masonry J. 12 (2): 24-37.

Malnotra, P. K. (2002) Cyclic demand spectrum. Earthquake Engineering and Structural

Dynamics, (31):1441-1457.

Morom 1996

Mosalam, K.M. (1996). Modelling of the non-linear Seismic behaviour of gravity load

designed infilled frames, 1995 EERI student Paper, Los Angeles, Calif.

Reinhorn, A. M., Madan, A.,Valles, R. E., Reichman, Y and Mander, J. B. (1995), Modelling

of masonry infill panels for structural analysis, NCEER-95-0018, Nat.Centre of Earthquake

Engineering, New York, Buffalo, N. Y.

Saneinejad, A., and Hobbs, B. (1995). Inelastic design of infilled frames. Journal of

Structural Engineering. ASCE, 121 (4): 634-650.

Smith, J.W. (1988), “Vibration of Structures”. Application in Civil Engineering Design.

London, Chapman and Hall, pp. 177-190.

10. Symbols aeff = Dependent effective peak acceleration

A b = Sectional area of beam

Ac = Sectional area of column

Ad = Area of equivalent diagonal strut.

As = Parameter varying the slip length due to crack opening in the panel

Cs = Seismic coefficient

DI = Cumulative damage parameter

fb = Brick compressive strength.

f m = Characteristic strength of straw bale wall.

Gk = Dead load

g = Acceleration due to gravity

h = Vertical dimension of in fill panel.

Ib = Moment of inertia of bean

Ic = Moment of inertia of column

Iw = Second moment of area of equivalent diagonal strut

In = normalized characteristics intensity

i = Instantaneous value.

Ko = Initial stiffness.

L = Lateral dimension of infill panel.

Ld = Length of the equivalent diagonal strut.

M = Total mass of the building and its contents

A A Adedeji

166

n = Transitional rates.

Qk = Live load

R = Ductility factor of the structure

{r} = Displacement vector

S = Seismic response factor

Sp1 ,Sp2 = Control the rate of deterioration for maximum and monotonic ductility respectively

Sk = Default value.

t =Thickness of infill panel.

tSD = significant duration of the accelerogram)

U = Ultimate load

Um = Corresponding maximum displacement.

Uy = Corresponding yield displacement.

V = Base shear

VD = Total dynamic base shear

Vm = Maximum lateral force.

Vy = Lateral yield force.

Vb = Total dynamic base shear

vg = peak ground velocity

Z = Hysteresis component.

b = Bond strength of straw bale [wall].

β = Constant that control the shape of the generated hysteresis

εm = Corresponding strain.

= Inclination of diagonal strut

i = Ductility

= Control parameter.

C = Basic compressive strength of straw bale

b = Shear stress of plain straw bale wall.

xy = Tangential stress