Collapse of infilled steel frames with semi-rigid connections

Collapse of infilled steel frames with semi-rigid connections

Proc. Instn Civ. Engrs Structs & Bldgs, 1998, 128, May, 103–111

A. Nadjai, BEng, MSc, PhD, MIStructE, PGCUT, and P. Kirby, BEng, PhD

Paper 11099

j The response of panels, consisting of semirigidly connected steel beams and columns with infilled shear panels, to lateral forces was evaluated using limit analysis. Thereafter a study was made of design methods, in order to incorporate such concepts in design examples. As a wide variety of connection types are used in practice, it is impractical to utilize the precise properties of individual connections. Therefore, a scheme is developed whereby connections are classified in terms of their strength and stiffness using moment–rotation data. The results from an investigation into the influence of these joints on the behaviour of structural panels are presented. Keywords: buildings, structures & design; brickwork & masonry; composite structures Notation B F H Mp f k m0 tw a gm gp j9c jc f

panel length collapse load panel height plastic moment capacity non-dimensional load-reduction factor ratio of ultimate moment of the joint to plastic moment of the beam non-dimensional ratio for frame/wall strength panel thickness panel reduction factor material safety factor penalty factor crushing stress effective crushing stress angle of rotation

Introduction Wood1 noted that, in a number of his tests, premature failure of joints occurred, indicating that the connections were weaker than the members that they were joining. May and Ma 2 extended this work to cover cases in which the ultimate moment capacity of the joints was lower than that of the connected members for precast concrete frames. The present work is an extension of May and Ma’s investigation of steel frames having semi-rigid joint connections between beams and columns. The important difference lies in the assumptions made about the rotational stiffness of the joints; that is, the extent to which the joints are able to transmit moments at various levels of rotation. Fig. 1 gives typical moment–rotation curves for skeletal steel

beam–column connections, from which it may be seen that even the simplest practical connection may possess significant rotational stiffness and be able to transfer moments between the connected members. 2. The growing body of research on connection behaviour has emphasized the advantage of including the connection characteristics for joints between beams and columns. Connections are basic elements and, as such, are integral parts of a steel frame, but are often the weakest part of a steel structure. A joint factor k can be introduced to specify the proportion of the actual moment capacity of the beam Mp that can be resisted by the connection. 3. Thus, the ultimate moment capacity of a semi-rigid joint connection can be written as kMp . This quantity will be significant when it is less than the ultimate moment capacity Mp of the weakest connected member:

Written discussion closes 28 August 1998

(a) when k $ 1, the joint is described as full strength, and (b) when k , 1, the joint is classified as partial strength. In addition to strength aspects, structural connections used to join beams and columns may be classified according to their rotational stiffness and, in design, the usual divisions are: (a) simple or pin jointed (zero stiffness), (b) semi-rigid, and (c) rigid (infinitely stiff). 4. The key to the development of a practical design method for infilled steel frames with semi-rigid joints is to classify the different types of connection used in a straightforward manner. It is desirable that connection responses are grouped according to broad ranges of flexural behaviour. The grouping must reflect the primary connection characteristics, and this leads naturally to the overall response types that have traditionally been associated with rigid, semirigid and flexible connections.

A. Nadjai, Lecturer, School of the Built Environment, Department of Civil and Structural Engineering, University of Ulster

Ultimate strength levels 5. A large volume of test data is now available covering a wide variety of beam–column connections, and in 1988 a computerized databank was established in the Department of Civil and Structural Engineering at the University of Sheffield. 3 The results of several tests carried out by Davison4 and extracted from the databank are shown in Fig. 2. The results are

P. Kirby, Senior Lecturer, Department of Civil and Structural Engineering, The University of Sheffield

103 Delivered by ICEVirtualLibrary.com to: IP: 193.61.145.22 On: Tue, 24 Aug 2010 11:23:23

Rigid

illustrated in Table 1 which indicates that it might be convenient to use ultimate moment magnitudes of 0·18 Mp and 0·75 Mp , for the pinned to partial strength and the partial strength to full strength boundaries, respectively, although for full strength connections it may be necessary to set the ultimate bending moment boundary higher than 0·75 Mp , perhaps even up to the full Mp of the beam.

Moment on joint

NADJAI AND KIRBY

Se

mi

-ri

gid

Limit analysis of panels

ð1Þ

Shear mode of infill panel 7. The infill is assumed to have the square yield criterion as shown in Fig. 3, where the stress axes are the principal stresses. This criterion was proposed by Nilson et al.,5 and has been used by Wood,1 May6 and Sims7 for the analysis of infilled frames. For a rigidly jointed infilled panel a basic shear mode S of collapse was proposed in which it was assumed that plastic hinges developed at the four corners of the bounding frame. This mode is also expected for an infilled frame with semi-rigid joints. The probability of the infill material behaving in an ideal, perfectly plastic manner is less than that of the surrounding frame, so a penalty factor gp was introduced by Wood. The penalty factor is applied to lower the crushing stress, j9c of the infill material to produce an effective crushing stress jc , such that jc ¼ gp j9c ;

gp , 1

ð2Þ

The factor gp is dependent on the relative strength of the infill material and bounding frame. An illustration of this parameter is given in Fig. 4 (taken from Wood1).

Rotation of joint

6jc /2, together with an accompanying hydrostatic stress of ¹ jc /2 as indicated in Fig. 5(a). Hence, equating the work done by the external loading to the energy dissipated in the frame and panel at the point of failure, the following equation is obtained: FHf ¼ 4kM p f þ 12 jc t w BHf

F¼

4 kM p 1 þ jc t w B 2 H

ð4Þ

Fig. 2. Moment–rotation curves for a variety of connection types: 1, web cleats to column web; 2, flange cleats to column flanges; 3, web and seat cleats to column flanges; 4, flush end-plate to column flanges; 5, flush end-plate to column web; 6, extended end-plate to stiffened column flanges

Mp of beam

80 70 60

6

50 5 40 30 4 20

3 2

10 0

1 0

5

Composite shear mode of infill and frame 8. May6 determined the upper bound solution for the S mode of collapse, in which the frame is assumed to sway by an angle f (Fig. 5(b)), with the formation of hinges at the four corners of the frame. For small displacements, a rectangular frame B 3 H will not require any expansion of the wall but only a pure shear strain f. This gives principal strains of 6f/2 and hence, from the normality rule and the yield criterion, the wall will have associated principal stresses of 0 and ¹ jc . In the xy coordinate system this leads to shear stresses of

ð3Þ

or

Moment: kN m

jMj # M p

Fig. 1. Typical moment– rotation curves for beam–column joints

Flexible

Yield criterion for frame 6. In this section the enclosing frames are assumed to behave in a rigid plastic manner with the yield criterion

10 Rotation: rad/1000

15

20

Table 1. Values of the ultimate moment k and a for various connection types Stiff

Typical Mu Typical k Factor a

Semi-rigid

Extended end-plate

Flush end-plate

0.75 Mp 0.75 2.0

0.36 Mp 0.36 2.5


Flexible Flange cleats

Web cleats

0.28 Mp 0.28 2.8

0.18 Mp 0.18 3.2

COLLAPSE OF INFILLED STEEL FRAMES

f¼

F ð4 M p =HÞ þ 12 jc t w B

Compression,

Define f as ð5Þ

and m0 by m0 ¼

8 Mp j c t w B2

f

b

0·04 f

b

ð6Þ

For the S mode of collapse, an upper bound is given by km0 ðB=HÞ þ 1 m0 ðB=HÞ þ 1

ð7Þ

A lower bound on the collapse load was also determined and found to be identical to the upper bound, provided that the hinges form at the corners in the bounding frame.

The design procedure 9. Thus a practical procedure for evaluating the strength of an infilled panel is the following straightforward procedure:

10. The values of gp are shown in Fig. 4 plotted against the nominal values of m0 using the full crushing strength jc . It is intended that the designer starts with nominal values of m0 (equation (6)), ascertains gp , to re-calculate m ¼ m0 /gp , then re-calculates f from equation (7), and finally calculates the collapse load in equation (8) using gp jc . The relevant gm is a material partial safety factor to allow for imperfections and to provide a reserve of strength. It is noted that BS 5628: Part 38 already provides an adequate margin of safety against the attainment of the ultimate limit state.

f

p=

2·663 m2 – 1·37 m + 0·46

p

0·4

p=

0·45

0·3 Test result (1) Design curve (1)

0·2 0·1 0

0

0·2

0·4

0·6 0·8 Nominal: m

1·0

1·2

Fig. 4. Penalty factor for brickwork. (From Wood 1 )

FH /2

kMp

kMp F

ct w /2

2kMp /H

2kMp /H ct w /2

ct w /2

2kMp /H

F

2kMp /H

ct w /2

kMp

kMp

Parametric study 11. The empirical penalty factor gp proposed by Wood has been criticized by some authors9¹12 who did several tests with different parameters not considered by Wood.1 The design method used by Wood is not always conservative and can given an overestimate of the value of the design collapse load, probably due to the fact that it attempts to suggest a universal criterion for all infill panels. 12. Several parameters have been investigated by Nadjai13 to adjust the expressions proposed by Wood for the design of collapse

Fig. 3. Square yield criterion for unreinforced walls

b

0·5

Penalty factor,

(a) Compute the value of m0 for the panel from equation (6). (b) Determine gp from Fig. 4. (c) Determine the factor k from Table 1. (d) Calculate f from equation (7) using m ¼ m0 /gp . (e) Evaluate the collapse load F using 4 kM p 1 jc F ¼f þ tw B ð8Þ 2 gm H

Compression, Tension

f¼

FH /2

(a)

FH /2 kM p

–kM p

F

ct w /2 ct w /2

ct w /2

F

ct w /2

Wall element

FH /2 (b)

Fig. 5. Shear mode S: (a) lower bound stress field; (b) upper bound mechanism


NADJAI AND KIRBY load. These are:

P

extended end-plates, flush end-plates, flange cleats, and web cleats.

2P

(b) The presence of infill in multistorey frames. (c) The presence of strong and weak infill in stiff and flexible steel frames. (d) The influence of variation in the elastic properties of the infill.

Analytical investigation 17. A two-storey infilled steel frame is presented to show that the presence of semi-rigid joints has an important influence on the behaviour of infilled frames. The steel frame used had material properties consistent with those of the frame tested by Davison.4 The columns were

3 @ 914·4 mm

Fig. 6. Stelmack’s steel frame (all members W5 3 16 A36 steel)

2743·2 mm

152 3 152 UC23 sections and the beams were 254 3 102 UB22 sections. A value of 210 kN/ mm 2 was assumed for the modulus of elasticity. The infill material was assumed to be uniform and to have mechanical properties corresponding to those of blockwork made of structural 100 mm thick solid blocks with 10 N/mm2 nominal strength using the material properties given by Riddington.16 The values of the shear stiffness and the coefficient of friction were taken from the shear box tests reported by King and Pandey.17 18. From the load–deformation curves shown in Fig. 10 it is seen that, in the elastic range, much of difference in the lateral deflection occurs due to the use of different types of connection; the beam–column joints have a significant influence on the behaviour of the steel structures as they directly control the lateral stiffness, the ultimate load of the structure. The load–drift curves of the frames (Fig. 10) illustrate the decrease in load-carrying capacity of the frame with increasing connection flexibility. 19. Not surprisingly, it was found during the analysis that the infilled steel frame structures


3600 mm

2800 mm

W8 × 31

Load

Block work t = 200 mm

Fig. 7. Dawe and Seah’s infilled steel frame

W10 × 39

Program validation 14. Among the several tests used in the validation are: (a) a small-scale steel open frame using semi-rigid connection (Fig. 6) tested by Stelmack14 and (b) a full-scale infilled steel frame rigidly jointed and pin connected (Fig. 7) tested by Dawe and Seah.15 15. Stelmack’s test frame, which consisted of a two-storey frames with flexible connections, was analysed using the present computer program. The joint connections were idealized with a trilinear representation of the real M ¹ f response. Fig. 8 shows the lateral load– displacement curves for the first and second storey, along with the predicted results. In general, the analytical load deflection curves agree reasonably well with the test results. 16. Dawe and Seah’s tests, in which the infilled frame was constructed and tested with rigid and pinned joint connections between the steel members. It is apparent from Fig. 9 that the use of a fully articulated frame results in a reduction in the ultimate load of over 50%. The major crack load is also reduced by about 25%. The analytical load–deflection curves shown in Fig. 9 agree reasonably well with Dawe and Seah’s test results. Although no test information is yet available for frames with semi-rigid joints and infill panels, it can be expected that the results for these frames will fall somewhere between those for the frames with rigid and pinned joints.

10·68 kN

W10 × 39

13. To investigate the above parameters, a computer program was developed by Nadjai13 using a non-linear finite-element approach, which takes into account the yielding of steel in both the members and the connections, cracking and crushing of the infill, and the non-linear interaction at the frame–infill boundary.

10·68 kN

1676·4 mm

(i) (ii) (iii) (iv)

1676·4 mm

(a) Types of semi-rigid beam–column connections:

COLLAPSE OF INFILLED STEEL FRAMES

where a is a panel reduction factor (discussed in the next section). 21. The use of a reduction factor a is reasonable because the behaviour of masonry in a frame is different from that which occurs in tests to determine its characteristic strength. The flow chart shown in Fig. 12 differentiates between ideal analyses and a practical design process, which needs to incorporate factors of safety to cater for practical variability in the form of values for gm . The factor a is then derived from a comparison of predicted and experimental test results. Table 1 gives indicative values derived from such computations using a very limited set of experimental values.

10

Load: kN

Tri-linear analysis 6

P 4 2P 2

0 (a) 25

20

Test result

15

Tri-linear analysis

P 10 2P 5

0 0

20

40 Deflection: mm (b)

60

80

Fig. 8. Comparison of the test results and the finite-element analysis results: (a) second storey; (b) first storey

Design examples

600 E2 500

Horizontal load: kN

Example 1 22. The method is demonstrated using the frame shown in Fig. 7, which was tested by Dawe and Seah.15 Two types of joint were considered: (a) flexible approximating to pinned, and (b) rigid. The corresponding experimentally observed ultimate capacity shear loads for the two frame–joint types were 267 and 556 kN, respectively. The infill panel was 3600 mm long and 2800 mm high. The panel consisted of 400 mm 3 200 mm 3 200 mm concrete blocks placed in running bond within a surrounding steel frame fabricated using W10 3 39 columns and a W8 3 31 beam. The plastic moment capacity of the beam was Mp ¼ 137 kN m. The characteristic strength of the blockwork jc was 8 N/ mm2 and the partial safety factor gm was taken as 1·0 for the calculation. 23. Remember that, in practice, gm would be

Test result

8

Load: kN

were capable of withstanding larger ultimate loads. The load–deflection curves (Fig. 11) show that in the initial stages of loading, when response is in the elastic range, there is not much difference between frames with different connections because the frame soon comes into contact with the infill panel, which stiffens the structure substantially. After a certain level of loading, the effect of joint response starts to become more significant. The load–drift curves of the frames (Fig. 11) illustrate that the loadcarrying capacity of the infilled frames increases with higher connection rigidity. 20. It is tentatively suggested, based on a limited parametric study and experimental tests, that Wood’s penalty factor might be relaxed. Experimental tests and analytical examples are used to demonstrate the predicted design collapse load using the hand method, and using a penalty factor. The new formula for the collapse load is 4 kM p 1 gp jc F¼ f þ tw B ð9Þ 2 a gm H

400

300 E4 200 Without opening Hinged frame 100

Finite-element analysis Finite-element analysis

0 0

5

10

15 20 Load point deflection: mm

25

30

Fig. 9. Comparison of the results of Dawe and Seah’s test with the finite-element analysis results


NADJAI AND KIRBY about 2·5, to cater for the inherent variability of the blockwork material. 24. Flexible joints without reduced penalty factor.

40

(a) Equation (6) gives

30

Rigid Extended end plate Flush end plate

Web cleats

8 3 137 3 106 ¼ 0:05 8 3 200 3 36002

(b) From Fig. 4, gp ¼ 0·32 and m ¼ 0·05/0·32 ¼ 0·16. (c) For a flexible joint, from Table 1 k ¼ 0·18. (d) Equation (7) gives 0:18 3 0:16 3 ð3:6=2:8Þ þ 1 f¼ ¼ 0:86 0:16ð3:6=2:8Þ þ 1

Load: kN

m0 ¼

Flange cleats

Pin 20

P 10

2P

ð10Þ 0

(e) The collapse load is, therefore,

(a) 40

4 3 0:18 3 137 F ¼ 0:86 2:8 1 þ 3 0:32 3 8 3 3:6 3 200 2

Rigid

P

Extended end plate Flush end plate

30

2P

Flange cleats Load: kN

¼ 0:86½35ðframeÞ þ 922ðwallÞÿ ¼ 952 kN

Web cleats Pin

20

This compares with a test value of 267 kN. 25. Note: The test results show that the formula gives an overestimate of the capacity of the wall if safety factors of 1 are used. The steel resistance is reliably known; therefore, any correction should be made to the panel strength and its interaction with steel. 26. The panel resistance is calculated as 0·86 3 922 ¼ 793 kN. The panel resistance expected is 267 ¹ (0·86 3 35) ¼ 237 kN. The reduced factor a calculated for pinned connections is a ¼ 793/237 ¼ 3·3. 27. Flexible joints with reduced penalty factor. Using the reduced factor a ¼ 3·3 equation (9), the collapse load is 4 3 0:18 3 137 1 0:32 F ¼ 0:86 þ 3 3 8 2:8 2 3:3 3 3:6 3 200 ¼ 0:86½35ðframeÞ þ 280ðwallÞÿ

10

0 0

5

Deflection, δ: cm (b)

10

(d) Equation (7) gives f¼

0:75 3 0:16 3 ð3:6=2:8Þ þ 1 ¼ 0:95 0:16ð3:6=2:8Þ þ 1

ð11Þ

(e) The collapse load is, therefore, 4 3 0:75 3 137 1 : : F ¼ 0 95 þ 3 0 32 3 8 2:8 2 3 3:6 3 200 ¼ 0:95½147ðframeÞ þ 922ðwallÞÿ

¼ 271 kN This compares with a test value of 267 kN is more practical then the partial safety factor is needed for such design hand method as proposed by Wood. 28. Rigid joints. Using a partial safety factor of 1 for the infill (gm ¼ 1·0) (a) As above. (b) As above. (c) For a rigid joint, from Table 1 k ¼ 0·75.

¼ 1016 kN This compares with a test value of 556 kN. 29. The panel resistance is calculated as 0·95 3 922 ¼ 876 kN. The panel resistance expected is 556 ¹ (0·95 3 147) ¼ 416 kN. The reduced factor a calculated with rigid connections is a ¼ 876/416 ¼ 2·1. 30. Rigid joints with reduced penalty factor. Using the reduced factor a ¼ 2·1 and equation


15

Fig. 10. Load–deflection behaviour of the twostorey frame with joints of varying stiffness: (a) first storey; (b) second storey

COLLAPSE OF INFILLED STEEL FRAMES (9), the collapse load is 4 3 0:75 3 137 1 0:32 þ 3 3 8 F ¼ 0:95 2:8 2 2:1 3 3:6 3 200

200

150

¼ 557 kN This compares better with the last value of 556 kN, then the value found by Wood’s method needs a reduction factor of over 2 to be more practical.

Load: kN

¼ 0:95½147ðframeÞ þ 439ðwallÞÿ 100

Extended end plate Flush end plate

50

Rigid joint connections

a ¼ 2:0

Extended end-plate

a ¼ 2:2

Flush end-plate

a ¼ 2:5

Flange cleats

a ¼ 2:8

Web cleats

a ¼ 3:2

More accurate values may well be related, not specifically to joint type, but to the ratio of joint strength and stiffness to panel strength and stiffness. However, there is a practical need to keep the method as simple as possible if it is to be developed into an approach accepted by practitioners.

Conclusions 34. The test and analysis results show that Wood’s method for pin jointed infilled frames without a penalty factor can give an overestimate of the capacity of a wall. The use of the penalty factor suggested by Wood can be

2P

Flange cleats Web cleats Pin 0 (a) 100 Rigid Extended end plate 80

Flush end plate Flange cleats Web cleats

60

Pin

Load: kN

Example 2 31. An analytical example was chosen from the parametric study 13 of one single infilled steel frame with different joint connections (Fig. 13). The connections selected are rigid, extended end-plate, flush end-plate, flange cleats, and web cleats with ultimate loadings of 197, 174, 150, 121 and 107 kN, respectively (Fig. 14). A comparison of the results obtained with design method and with the analysis is given in Table 2. 32. It can be seen from Table 2 that the hand design method gives a gross overestimate of the capacity of the wall if a penalty factor gp of 0·37 is used with no further reduction factor. Although the connections constitute only a small portion of the steel frame, their effect is significant in the overall structural performance (Table 2). For example, the ultimate resistance of the infilled frame is reduced by about 46% due to a change from fully rigid to web cleat joints. 33. Bearing in mind the need for simple values for the reduction factor a, an analysis of the results has led the following tentative suggestions for suitable values:

P

Rigid

P 40

2P 20

0 0

10

20 30 Deflection, : mm (b)

conservative if used for frames with the full spectrum of joints, as the characteristics of joints between beams and columns is very influential on the response of such a structure. 35. The main aim of this investigation was to suggest a design method for infilled steel frames having any type of beam–column connection. A simple system for the classification of steel beam–column connections in terms of stiffness and ultimate strength has been presented that is practical for use by designers and fabricators of structural steel building structures because it does not require the use of detailed connection performance data. 36. It has been demonstrated that the type of joint connection has an important influence on the capacity of the composite structure. The results presented show that there are substantial benefits to be gained from including the effects of beam–column connections in the calculation of the strength of these structural frames.

40

50

Fig. 11. Effect of connection flexibility on the behaviour of the infilled frame: (a) first storey; (b) second storey


NADJAI AND KIRBY

Design of collapse load

Experimental and analytical work

Site work

BS 5628: Part 3: 1978 gm ¼ 1·0

gm ¼ 2·5–3·1 special gm ¼ 2·8–3·5 normal

m0 ¼

8 Mp gm j c tw B 2

Penalty factor gp from Fig. 4

m¼

m0 gp

Joint connection factor k from Table 1

Load factor

f¼

kM ðB =H Þ þ 1 m ðB = H Þ þ 1

Reduced factor

a from Table 1

a ¼ Load(calc.)–Load(exp.)

F ¼f

4 kMp 1 gp jc þ t B 2 a gm w H

Fig. 12. Flow chart of the design procedure

Table 2. Ultimate load values obtained with the design method and with finite-element analysis

Joint type Rigid Extended end-plate Flush end-plate Flange cleats Web cleats

Joint factor, k

Load factor, f

Penalty factor, gp

Reduction factor, a

1.0 0.75 0.36 0.28 0.18

1.0 0.98 0.95 0.94 0.93

0.37 0.37 0.37 0.37 0.37

2.0 2.2 2.5 2.8 3.2


Design failure load, F: kN Without a

With a

Calculated failure load, F

679 652 611 600 588

208 177 156 135 112

197 174 150 125 107

COLLAPSE OF INFILLED STEEL FRAMES 200

Rigid

150

Extended end plate

Load: kN

Flush end plate

EF = 210 kN/mm2 EW = 15·40 kN/mm2 Mp = 74·67 kN/mm2 t w = 100 mm v = 0·15

3600 mm

152 × 152 × 23 UC

Semi-rigid joint

152 × 152 × 23 UC

254 × 102 × 22 UB

P

Flange cleats 100

Web cleats

P

50

0 0

4953 mm

Fig. 13. Infilled steel frame with semi-rigid joint connections

20 30 Deflection, : mm

40

50

Fig. 14. Results of the finite-element method

References 1. WOOD R. H. Plastic composite action and collapse design of unreinforced shear wall panel in frames. Proceedings of the Institution of Civil Engineers, 1978, 65, 381–411. 2. MAY I. M. and MA S. Y. A. Collapse loads for unreinforced panels with weak joints. International Journal of Masonry Construction, 1982, 2, 109–114. 3. WANG Y. C. Semi-rigid Action in Steel Frame Structures: Data-bank of Mf Test Results. Department of Civil and Structural Engineering, University of Sheffield, 1990, ECCS Agreement No. 7210 SA/189. 4. DAVISON J. B. Strength of beam–column in flexibly connected steel frames. PhD Thesis, University of Sheffield, 1987. 5. NILSON M. P. et al. Concrete plasticity. Danish Society for Structural Science and Engineering, Lyngby, 1978. 6. MAY I. M. Determination of collapse loads for unreinforced panels with and without openings. Proceedings of the Institution of Civil Engineers, 1981, 71, 215–233. 7. SIMS P. A. C. Plastic Analysis of Reinforced Concrete Panels in Frames, Plasticity in Reinforced Concrete. Final report, IABSE Coloquium, Copenhagen, 1979, 95–102. 8. BRITISH STANDARDS INSTITUTION Code of Practice for Structural Use of Masonry. Part 1: Unreinforced

10

9.

10. 11.

12. 13.

14.

15.

16.

17.

Masonry. BSI, Milton Keynes, 1978, BS 5628, Part 1. SAMAI M. L. Behaviour of Reinforced Concrete Frames with Lightweight Blockwork Infill Panels. PhD thesis, University of Sheffield, 1984. MA S. Y. A. Unreinforced Shear Wall Panels in Frames. PhD thesis, University of Warwick, 1983. NAJI J. H. Non-linear Finite Element Analysis of Reinforced Concrete Panels and Infilled Monotonic and Cyclic Loading. PhD thesis, University of Bradford, 1989. ABOLGHASEM S. Non-linear Analysis of Infilled Frames. PhD thesis, University of Sheffield, 1990. NADJAI A. The Behaviour of Steel Frames with Semirigid Joints Containing Unreinforced Infill Panels. PhD thesis, University of Sheffield, 1993. STELMACK T. W. Analytical and Experimental Response of Flexibly Connected Steel Frames. MS thesis, University of Colorado, Boulder, 1982. DAWE J. L. and SEAH C. K. Behaviour of infilled steel frames. Canadian Journal of Civil Engineering, 1989, 16, No. 6, 865–876. RIDDINGTON J. R. The influence of initial gaps on infilled frames behaviour. Proceedings of the Institution of Civil Engineers, 1984, 77, 295– 310. KING G. J. W. and PANDEY P. C. The analysis of infilled frames using finite elements. Proceedings of the Institution of Civil Engineers, 1978, 65, 749– 760.
