DEVELOPMENT OF RELIABILITY ASSESSMENT SOFTWARE · PDF fileDEVELOPMENT OF RELIABILITY...

15th International Brick and Block

Masonry Conference

Florianópolis – Brazil – 2012

DEVELOPMENT OF RELIABILITY ASSESSMENT SOFTWARE FOR EXISTING

MASONRY BUILDINGS SUPPORTED BY REINFORCED CONCRETE FRAMES

Gu, Xianglin1; Sun, Dongjie

2; Sun, Kai

3; Peng, Bin

4

1 PhD, Professor, Tongji University, Department of Building Engineering, [email protected]

2Post Graduate Student, Tongji University, Department of Building Engineering, [email protected]

3 Master, Tongrui Civil Engineering Technology Company, [email protected]

4 PhD, Associate Professor, University of Shanghai for Science and Technology, School of Environment and

Architecture, [email protected]

A Masonry Assessment software Package (MAP) with three modules of pre-processing, core

analyzing, and post-processing was developed based on the characteristics of the masonry

building structures supported by reinforced concrete frames. The software can be used to

calculate the internal forces, bearing capacity, deformation and cracking width of masonry

walls, beams, columns in an existing building considering the interaction between the

masonry structure and the supported reinforced concrete frame structure. Based on the

calculation and the inspection results, the reliability grades of both elements and the structure

in the building can be assessed automatically, and finally the assessment report text and

graphic display contents can be output. Through the application of the software for the

reliability assessment of an existing building structure, the software was verified and the

results showed that the software is applicable for the reliability assessment of existing

masonry buildings supported by reinforced concrete frames and it is a convenient assistant

tool for engineers. In this paper, the details of development technology, application and

verification for the software are introduced.

Keywords: Masonry structure, frame, reliability, software, existing buildings

INTRODUCTION

For the reasons of low cost and convenient construction, multi-story masonry buildings

supported by reinforced concrete frames are widely used in China, especially for the buildings

along the streets (Figure 1). Different from the traditional masonry building structures, the

lateral stiffness of the structure in a masonry building supported by reinforced concrete frames

is not evenly distributed along the height of the building. The stiffness of the masonry

structure in a building is larger, but the stiffness of supported frames at the bottom of the

building is usually smaller. Under external loads, this kind of structure may have stress

concentration in the position where the lateral stiffness has an abrupt change, and it will cause

large deformation. This will eventually lead to the severe damage of the structure, especially

in earthquakes (Figure 2).

After serving for a long period, the mechanical performance of existing buildings will

deteriorate more or less. Besides, because of the complexity and specificity of this kind of


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structure, some of the existing buildings can not meet the requirements of current Chinese

codes. It is necessary to have an inspection and assessment on existing buildings to guarantee

the safety and serviceability. Usually, a lot of calculations and analyses are needed in the

assessment. Therefore, it is significant to develop applicable software for the reliability

assessment. This is just the objective of the paper, and in the following sections the short

name MAP for the Masonry Assessment software Package developed by the author will be

used.

Figure 1: Building along the street Figure2: Building damaged in an earthquake

SYSTEM AND FUNCTIONS OF THE SOFTWARE

There are three modules in MAP, which are pre-processing, core analyzing, and post-

processing. In the pre-processing, data including axis network information, geometrical and

material information of members, storey information, load information and so on, are

supplied to the core analyzing by the way of direct input and the way of graphic input

methods. The module supports the operations of undo and redo, and both two-dimensional

and three dimensional views can be displayed (Figure 3), which is convenient for users to

build the calculation and analysis models. The main tasks for core analyzing module are

model checking, structural analyzing, reliability assessment, and so on. The post-processing

module includes two parts, text output and graphic display, which are convenient for users to

use the results.

Figure 3: Interface of MAP


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The main functions of MAP are shown in Figure 4. Not only the main structural elements,

such as masonry walls, masonry columns, concrete beams, concrete columns, concrete slabs,

shear walls and foundations, but also the other elements, including ring beams, structural

columns, lintels, wall columns, plates below beams, cantilever beams can be analysed by

using MAP to calculate the internal forces and capacity of elements, and determine the

structural information, such as the ratio of the height to the sectional thickness of a wall.

Except the plain masonry walls, both the reinforced masonry walls and masonry composite

walls with structural columns can be analysed in MAP. After calculating the compression of

walls, an additional checking for the walls at the corner can be conducted by the angular

cross-section method, which used the composite section of the crossed walls. The local

compression below all kinds of beams can be considered in MAP to ensure the safety of the

masonry walls. The bearing capacity of lintels and the overturning of the cantilever beams can

also be calculated. For foundations and subgrade, the bending and punching capacity of the

foundations, the subgrade capacity and the settlements can be checked. Finally, the reliability

grades of structural members and structural system can be assessed according to the

calculating results and structural measures.

MAP

Pre-

proce-

ssing

Core

Analyz-

ing

Grid

Information

Geometric

information

Material

Information

Load

Information

Storey

Information

Model Check

Structural Analysis

Reliability

Assessment

Text Output

Graphic Display

Post-

proce-

ssing

Model Display

Data Input

Graphic Input

Two-

dimensional

Views

Three

dimensional

Views

Part of Masonry

Structure

Part of Frame

Structure

Foundation and

Subgrade

Assessment of

Members

Assessment of

the Structure

Safety

Suitability

Durability

Ratio of Height to

Sectional Thickness

of

a Wall

Capacity of Walls

Other Members

Static Analysis

Dynamic Analysis

Capacity of

Foundations

Capacity of

Subgrade

Settlement of

Subgrade

Compression

Shearing

Bending

Local Compression

below Beams

Lintel Checking

Cantilever Beam

Checking

Bending

Punching

Figure 4: System and functions of MAP


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KEY TECHNOLOGY IN THE SOFTWARE

Structural Analysis Linear structural analysis method for existing masonry buildings

supported by reinforced concrete frames was used in MAP. Figure 5 shows the model to

analyse a masonry wall supported by a reinforced concrete frame. The upper part, the

masonry wall, can be analysed by using force equilibrium condition, and the lower part, the

reinforced concrete frame, can be analysed by using the finite element method. Under

earthquake, the internal forces caused by earthquake action can be calculated by both the base

shear method and the response spectrum method.

Hn

Hi

H1

Figure 5: Model to analyse a masonry wall supported by a reinforced concrete frame

Distribution of Interlayer Shearing Force The interlayer shearing force caused by the

earthquake is distributed to the structural members based on the type of the floor structure.

When the floor is rigid, such as the in-situ cast reinforced concrete floor, the interlayer

shearing force is distributed according to the equivalent stiffness values of walls (Equation 1).

When the floor is flexible, such as the wooden floor, the interlayer shearing force is

distributed according to the representative values of the gravity load born by walls (Equation

2). When the floor is semi-rigid, such as the prefabricated reinforced concrete floor, the

interlayer shearing force is distributed according to Equation 3.

imim i

ik

1

n

k

KV V

K

(1)

imim i

i

GV V

G (2)

im imim i

i i

1

2

K GV V

K G

(3)

Where, Vim is the shearing force distributed to a structural member, Vi is the interlayer

shearing force of a storey, Kim and Kik are the equivalent stiffness of a wall, Gim is the

representative value of the gravity load born by a wall, Gi is the representative value of the

gravity load of the whole storey.

In the first floor, the interlayer shearing force is distributed to the columns according to their

lateral stiffness (Equation 4).

Fn

Fi

F1

Gn

Gi

G1

Fn

Fi

Gn

Gi

i

2

n

i

V F

i

2

n

i

N G

i i 1

2

( )n

i

M F H H

M

1F F V


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imrimr im

imt

1

s

t

KV V

K

(4)

Where, Vimr is the shearing force distributed to the calculating unit, Kimr and Kimt are the

equivalent stiffnesses of the calculating unit, s is the number of the calculating units

belonging to the entire storey.

Seismic Force of the Supported Frame The seismic forces of the supported frame include

the shearing force and the overturning moment which are shown in Figure 5. Because the

lateral stiffness of the upper masonry wall is larger than that of the lower supported frame, the

shearing force born by the supported frame should be multiplied by an amplifying coefficient

between 1.2 and 1.5 which is determined by k

, where γk is the ratio of the lateral stiffness

of the masonry wall to that of the supported frame. The overturning moment is generated by

the horizontal forces applied on the upper masonry wall. Knowing the overturning moment,

the axial forces in supported columns can be easily calculated. For example, when the

earthquake direction is parallel to the X axis in Figure 6, the vertical force of a supported

column is:

y i i i

i2

k y0k k k

1

( )

[ ( ) ]n

k

M E A X aN

E I A X a

(5)

Where, My is the overturning moment of the frame in X direction; Ei or Ek is the elastic

modulus of a column, Ai or Ak is the sectional area of a column, Xi or Xk is the coordinate of

the center of a column in X direction; a is the coordinate of the storey center in X direction,

Iy0k is the moment of inertia of a column.

Y

X

x

yy

x

a

b

Figure 6: Coordinate system of a structure

Adjustment of Internal Forces of Wall Beams The beams of the frame and the supported

wall can be considered as a composite structural member. Because of the arch effect of the

wall, the value of moment and shearing force in top frame beams can be reduced both at the

span middle and the support end, and longitudinal tensile forces should be added to the beams

correspondingly. Therefore, the beams are actually subjected to axial tension and bending.

Assessment of Structures The safety of elements is assessed based on four items of bearing

capacity, structural measures, unsuitable displacement and cracking status. There are four


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grades (au to du) for each item, which can be determined based on the reliability analysis

results. For example, the grade of bearing capacity of structural members, including the

concrete and masonry members, can be calculated according to Table 1, where R is the value

of bearing capacity, S is the value of internal force, γR is the partial coefficient, γ0 is the

coefficient of importance. The minimum grade among four items is regarded as the safety

grade of a structural member. The suitability of a structural element is assessed based on three

items of displacement, non-stress cracking, and air-slake. Also the minimum grade is regarded

as the suitability grade for a structural member. Finally, the smaller value between the safety

and suitability grade is taken as the reliability grade for a structural member. If we take into

account the performance deterioration of structural members with time, the durability of a

structural member can also be assessed. After finishing the assessment for all the structural

members, the software can give a reliability grade for the whole structural system. In Figure 7,

the safety, or suitability, or durability grade for every storey of a structure (Au ~ Du for the

safety, As ~ Cs for the suitability, and Ad ~ Bd for the durability) is assessed first, then the

grade for the structural system will be calculated according to the assessment results of each

storey and the relations among storeys.

Table 1: Bearing capacity grade of concrete and masonry members performance Capacity Grade au bu cu du

R/γ0γRS ≥1.0 ≥0.95 and <1.0 ≥0.90 and <0.95 <0.90

Begin

Calculate the Weight

Coefficient of Each

Element

ωi=ri/Σrini

Γj=Σωij

N

N

Du

Au

Bu

Cu

Y

Y

End

j =Total storey number

N

Y


Σrini

Storey j

Γbu≤0.25，Γcu=0，Γdu=0

Γcu≤0.15，Γdu=0

Γdu≤0.05

N

Y

j = j +1

Begin


Coefficient of Each

Element

ωi=ri/Σrini

Γj=Σωij

N

Cs

As

Bs

Y

Y

End

j = Total storey number

N

Y


Σrini

Storey j

Γbs≤0.35，Γcs=0

Γcs≤0.25

N

j = j +1

Begin


Coefficient of Each

Element

ωi=ri/Σrini

Γj=Σωij

Bd

Ad

Y

End

j = Total storey numberN

Y


Σrini

Storey j

Γbd≤0.20

N

j = j +1

Safety Suitability Durability

Figure 7: Reliability assessment for structural system


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APPLICATION OF THE SOFTWARE

Figure 8 is a typically masonry building supported by reinforced concrete frames. It was built

in 1995. The whole area of the building is 2170mm2, the height of the first storey is 4350 mm,

and the height of each other storey is 3400mm, the total height of the building is 18250 mm.

The first storey of the building is reinforced concrete frame structure, and the four storeys

above are masonry structure. In the first storey, there are 10 spans in longitudinal direction,

the column spacing is 3000–3900mm, and there are 3 spans in transverse direction, the

column spacing is 4000–6900mm. The size of column section is 300×300mm or 400×600mm. The spacing of rigid transverse walls of upper part is 3000-6900mm, the width of the

corridor is 1800mm, and the spacing between longitudinal walls of rooms is 5100mm. The

sectional thicknesses of walls are all 240 mm. All of walls were constructed with fired

common bricks and composite mortar. The strength values of materials are shown in the

Table 2 according to the inspection results. There are structural columns located at the corners

of external walls and stairs, and there are also ring beams located above all of the bearing

walls. The first storey is the cast in-situ reinforced concrete floor, and the second to fifth

storeys are the prefabricated reinforced concrete floors. The structural planes of the 1st and 2

nd

storey are shown in Figure 10 and Figure 11. Figure 9 is the image of the model built with

MAP.

Table 2: Strength of materials

Storey Compressive strength

of concrete (MPa)

Compressive strength

of mortar (MPa)

Compressive strength

of brick (MPa)

1 38.6 —— ——

2 20.3 12.7 10.0

3 20.3 8.5 10.0

4 20.3 8.5 10.0

5 20.3 8.5 10.0

Figure 8: Photo of a building Figure 9: Image of the model built with MAP

Figure 12 gives the assessment results for structural members on the 2nd

storey according to

the compressive capacities of walls. In Figure 12, the upper values are the ratios of capacity to

the partial coefficient, that is R/γR, and the lower values are the internal forces multiplied with

the coefficient of importance, that is γ0S. All of the ratios of R/γ0γRS are larger than 1.0, so the

safety grade of the walls in the 2nd

storey are au.


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LL2(10) 250x800

LL1(10) 300x700

LL1(10) 300x700

LL1(6) 300x700 LL1(2) 300x700

KJ-

2(2

) 4

00

x1

20

0

KJ-

1(3

) 4

00

x1

20

0

KJ-

1(3

) 4

00

x1

20

0

KJ-

1(3

) 4

00

x1

20

0

KJ-

1(3

) 4

00

x1

20

0

KJ-

1(3

) 4

00

x1

20

0

KJ-

1(3

) 4

00

x1

20

0

KJ-

1(3

) 4

00

x1

20

0

KJ-

2(2

) 4

00

x1

20

0

KJ-

2(2

) 4

00

x1

20

0

KJ-

2(2

) 4

00

x1

20

0

QL

QL

25

0x

40

0

LL3(6) 250x1000

25

0x

40

0

25

0x

40

0

25

0x

40

0

25

0x

40

0

25

0x

40

0

25

0x

40

0

QL

QL

L11 240x400

L1

2 2

40

x3

00

YP1

YP

2

51

00

18

00

51

00

40

00

16

00

0

3000 3900 3900 3900 3900 3900 3900 3000 3600 330036300

3000 3900 3900 3900 3900 3900 3900 3000 3600 330036300

51

00

18

00

51

00

12

00

28

00

16

00

0

4.160

Figure 10: Structural plane of the 1

st storey

GL GL GL GL GL GL

GL GL GL GL GL

GL GL GL GL GL GL

GL

GL

GL GL

GL

GL

GL

GL

GL

GL GL GL

GL

GL GL GL GL GL GL

QL

GL

L22(2) 250x700

L22(2) 250x700

L21(2

) 400x950

L23 3

00x750

L24 250x350

QL 240x240

QL

QL

QL

QL

GL

GL

GL

弯)

L25 150x300 YZB

YZB

YZB

YZB

YZB Y

ZB

YZB

YZ

B

YZB

YZB

YZB

YZB

YZB

YZB

YZ

B

YZB

B2(

100) B

3(10

0)

B1(100)B1(100)

B1(100)B1(100)

B1(100)

B1(100)

B1(100)B1

B1(100) B1

Z

Z

Z

51

00

18

00

51

00

120

00

3000 3900 3900 3900 3900 3900 3900 3000 3600 330036300

3000 3900 3900 3900 3900 3900 3900 3000 3600 330036300

51

00

18

00

51

00

12

00

132

00

7.560

Figure 11: Structural plane of the 2nd

storey

Figure 13 is the bending moment diagram of the 1st storey. In order to make the graphic

display more clearly, the author closed the show of the results of the elements which are

parallel to the X coordinate. All the values of moment were adjusted because they are parts of

wall beams, just as illustrated before.


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Figure 12: Compressive capacity assessment of walls in the 2

nd storey

Figure 13: Bending moment diagram of beams in the 1

st storey

The safety grade of each structural element is au, which is the top grade, so the safety grade of

each storey is Au, accordingly, the safety grade for structural system is Au too, which matches

the real situation of the building.

CONCLUDING REMARKS

Assessment of existing buildings is different from the design of new buildings. Special

technology should be used in practice. With the help of an unique software, engineers can

inspect and assess the behaviour of existing building structures more efficiently. As a

specified software, MAP developed by the authors can be well used to assess the reliability of

existing masonry buildings supported by reinforced concrete frames to increase the accuracy

and the efficiency of the assessment. In the future, the software will be modified to suitable

for the reliability assessment for other kinds of existing building structures.

ACKNOWLEDGEMENTS

This work was funded by the National Key Technology R & D Program of China (Grant No

is 2006BAJ03A07).

REFERENCES

DG/TJ08-804-2005, Standard of structural inspection and assessment for existing buildings

GB 50011-2010, Code for seismic design of buildings


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Gu, X L, Chen, S J, and Zhang, W P. “Practical method of assessing reliability of structural

system of existing buildings.” Structural Engineers. 23, 2007, 12-17. (in Chinese)

Gu, X.L., Sun, D.J. ”Development and Application of Reliability Assessment Software for

Historic Masonry Structures”. Advanced Materials Research, Part 2., 2010, pp 1271-1276.

Gu, X L, Xu, Y, and Zhang, W P. “Safety analysis of elements in existing buildings.” Journal

of Building Structures. 25, 2004, 117-122. (in Chinese)

Li S B, Wang, J G, and Xie, H C. “Development of reliability assessment software for

existing buildings.” Journal of Chongqing Polytechnic College. 17, 2002, 13-14. (in Chinese)

Lu X L, Zhou, D Y, and Li, S M. “Theories and instances of seismic design for building

structures.” Shanghai, China: Tongji University Press, 2002, 93-111. (in Chinese)

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