Seismic behavior of energy-saving block & invisible multi-ribbed frame walls with different sizes of openings

Abstract

To build the design method of new energy-saving block & invisible multi-ribbed frame composite walls developed by our research team, taking window and door openings of various dimensions as the parameters of the experimental study, six 1/2 scaled energy-saving block & invisible multi-ribbed frame composite wall specimens were made. The cyclic loading tests on specimens were performed. The failure characteristic, hysteretic behavior, ductility, energy dissipation capacity and stiffness degradation were investigated. The test results show that as window and door openings increase, integrity of the wall weaken, causing bearing capacity of the wall to decline, degrading the stiffness more slowly after yield, the limit displacement to be bigger, ductility to be good, energy dissipation capacity increased. The above results indicated that to rigid walls, when the bearing capacity does not decrease obviously, with appropriated opening, the seismic behavior of the wall can be greatly improved. Based on the analysis and comparison of test data, deformation limit of the wall under different performance objectives are determined, which provides the basis for the establishment of design method of the wall.

Keywords

Energy-saving block & invisible multi-ribbed frame composite walls size of openings stiffness ductility energy dissipation deformation limit

1. Introduction

As one of series research of our project team, this paper studied the hysteretic behavior, ductility, stiffness degradation, energy dissipation capacity and other seismic behavior of the energy-saving block & invisible multi-ribbed frame composite walls under different sizes of openings. Many domestic and overseas scholars have studied the seismic performance of other walls under different sizes of openings. Wu et al. [1] made a seismic performance test of four full-size concrete frame restricted and transverse opening interlocked block dry-laid wall under the action of constant vertical loads and horizontal low cyclic loads, and analyzed the influence of window opening on the seismic performance of wall. The test results indicate that the window opening reduces the initial cracking load, the ultimate load and stiffness of the walls. Chang et al. [2] studied the influence of the opening position and size of multi-ribbed composite wall, and figured out the lateral stiffness of the multi-ribbed composite wall with opening by introducing the opening reduction coefficient. Jia et al. [3]discussed the influence of the changed size and position of opening on the seismic performance of wall on basis of ANSYS, a finite element analytical model. Wu et al. [4] made a horizontal low cyclic load test of seven external prestressing rough-dressed stone masonry walls and studied the influence of window openings and other parameters on the stress process, failure mode, shear bearing capacity and hysteretic curve of the walls. Zhang et al. [5] built a finite element model of masonry wall based on ABAQUS, and verified the established numeric values to analyze the applicability of model through a comparison of test wall; utilized the established model to investigate the influence of opening condition and other factors on the seismic performance of masonry wall. Su et al. [6] combined with the test data of a lot of domestic and overseas single-layer single-span infilled wall’s RC frame model, analyzed the influence of opening on the ultimate lateral bearing capacity and original stiffness of infilled wall’s RC frame, and provided the corresponding calculation method of reduction coefficient. Hosseinzadeh and Tehranizadeh [7] studied the nonlinear behavior of the steel plate shear wall with reinforced large rectangular opening (used as the window or door of a building). The numerical analysis was also conducted to a large number of steel plate shear walls with or without openings, and the analytical results: (1) reveal the characteristics of steel plate shear wall with openings; (2) study the influence of different opening characteristics as well as the size of components in the local boundary around the opening; and (3) discuss the introduction of openings that result in the change of strength, stiffness and ductility of the wall. Penava et al. [8] built a calculation model base on non-linear finite element, and the calculation model was verified by a series of tests. Thereby, an investigation was made on expanded parameters as well as the influence of different window and door sizes and positions on the shear behavior of infilled wall’s frame. Hussein et al. [9] manufactured a full-size wall assembly made of six clay masonry wallboard, 2 constraint column and one binder, and push down under the action of constant vertical loads and monotonic horizontal loads. The wallboard has different structure, i.e. solid wall and the wall with window or door openings.

Above research can be used for reference by this paper, but the studied energy-saving block & invisible multi-ribbed frame walls have their own characteristics, especially the research of its seismic performance with different sizes of openings is a new topic. Therefore, in this paper, the seismic performance of 1/2 scaled wall specimen with six different sizes of openings was investigated through low cyclic load test.

2. Test profile

2.1 Specimen design and reinforcement

The test specimen designed was divided into two groups. The 1/2 scaled model was selected.

The first group consists of three door opening specimen with different sizes, and the wall dimension is 2.7 m $\times$ 1.35 m, numbered by MDW-1, MDW-2 and MDW-3. The opening size (hole ratio) is 450 mm $\times$ 1050 mm (12.9%), 600 mm $\times$ 1050 mm (17.3%) and 750 mm $\times$ 1050 mm (21.6%).

The second group consists of three window opening specimen with different sizes, and the wall dimension is 1.8 m $\times$ 1.35 m, numbered by CDW-1, CDW-2 and CDW-3. The opening size (hole ratio) is 600 mm $\times$ 750 mm (18.5%), 750 mm $\times$ 750 mm (23.1%) and 900 mm $\times$ 750 mm (27.7%).

The specimen takes ratio of holes as change parameter (hole ratio is the ratio of opening area to specimen’s gross area), and according to the optimal reinforcement ratio obtained by the research team in previous studies, the reinforcement rate of six specimens remains unchanged. The specimen size and reinforcement are shown in Fig. 1.

Table 1
Mechanical properties of steel reinforcement

Steel reinforcement	Diameter (mm)	Yield strength (MPa)	Ultimate strength (MPa)	Elasticity modulus (N/mm ${}^{2}$ )
$\phi$ 6	6	432.7	578.6	2.05 $\times$ 10 ${}^{5}$
$\phi$ 8	8	407.6	525.3	2.08 $\times$ 10 ${}^{5}$
$\phi$ 10	10	428.6	517.6	2.13 $\times$ 10 ${}^{5}$

Table 2

Physical and mechanical properties of the block

Block material	Compressive strength (MPa)	Tensile strength (MPa)	Elasticity modulus (N/mm ${}^{2}$ )
FGD gypsum	15.8	1.6	1950

Table 3

Mechanical properties of fine aggregate concrete

Specimen no.	Component	Designed strength grade	$f_{cu,m}$ (MPa)
MDW-1	Multi-ribbed frame	C20	21.03
MDW-2	Multi-ribbed frame	C20	20.50
MDW-3	Multi-ribbed frame	C20	19.37
CDW-1	Multi-ribbed frame	C20	21.49
CDW-2	Multi-ribbed frame	C20	20.58
CDW-3	Multi-ribbed frame	C20	21.07

Figure 1.

Sizes and reinforcement of specimens.

2.2 Mechanical properties of specimen materials

The measured values of the mechanical properties [10] of steel reinforcement used in the specimen are shown in Table 1; the measured values of the physical and mechanical properties of the block are shown in Table 2, and the measured values of the mechanical properties [11] of fine aggregate concrete are shown in Table 3.

2.3 Lading set-up and loading process

500 kN MTS actuator is adopted. Four round steel of the top beam of specimen are connected with actuator by conversion steel plate. Two ends of the floor beam of specimen are fixed at prepared holes on the ground by pressing beam respectively. Two terminal parts of the floor beam are fixed by using jack with precompression. The schematic diagram of the lading set-up is shown in Fig. 2 (take the first group of specimens as an example).

Figure 2.

Lading set-up.

The loading process is an important controlling unit in the control of loading and the simulation of seismic oscillation. This test uses variable-amplitude displacement control [12] for loading. Before the specimen yields, each loading stage repeats twice, until the load value decreases below 85% of the maximum bearing capacity. Then the specimen is deemed as failed, and the loading can be stopped. The loading process of each specimen is shown in Fig. 3.

2.4 Test plan

Displacement test: the layout of displacement meter is shown in Fig. 2. A laser displacement meter is set at the end of the loading direction of the top beam, to measure the horizontal displacement of top beam; a displacement meter is set inside the wall surface at 1/3 and 2/3 of the wall height, to monitor the deformation of the wall under force; in order to eliminate the influence of the movement or rotation of floor beam on the overall displacement of the wall, the displacement meters are set in the horizontal and vertical directions of floor beam within the loading plane, to monitor the slippage and warping deformation of floor beam.

Figure 3.

Loading process of specimens.

Strain test: it is preliminarily judged that the failure mode of the specimen is roughly a shear failure, and the cracks are distributed in a crossing way. In order to measure the strain of the reinforcement of the ribbed beam and column, the strain gauge is arranged in the cross position. The arrangement of strain measuring points of the first and second groups of specimens are shown in Fig. 4.

Figure 4.

Strain measuring point of specimens.

3. Test phenomenon and failure mode analysis

3.1 Test phenomenon of the first group of specimens

Take the specimen MDW-1 as an example. No crack exists before specimen is loaded. When the displacement amplitude of 1.35 mm is loaded in a forward direction, and the peak load value of this stage is 71.6 kN, about 41.8% of the ultimate load value, at this time, the first “ $\backslash$ ” shape crack appears in the middle of the second skin block wall on the left side of the door opening and on the left near the inner side of the left wing wall, with crack width of 0.2 mm and length of 6 cm. This stage is reversely loaded, with peak load value of $-$ 50 kN, and three “/” shape micro-cracks appear at the door opening in the middle part of the wall, with crack width of 0.3 mm and length of 5 cm. When the displacement amplitude of 2.75 mm is loaded in a forward direction, and the peak load value is 120.7 kN, multiple “ $\backslash$ ” shape cracks appear, most of which are distributed in the upper left and lower right corner of the wall, and original cracks continue to widen and extend close to the edge of the block, but it does not form a crack through ribbed beam. This stage is reversely loaded to the peak load of $-$ 85 kN, and multiple “/” shape cracks appear, most of which are distributed in the lower left and upper right corners of the wall. They roughly form an “X” shape with forward loaded cracks, with only a few overlaps, which have not been connected yet. There are two obvious “/” shape cracks on the wall near the lintel at the top left of the door opening, with crack width of 0.8 mm. When the fourth-stage displacement (5.4 mm) is forward loaded to the peak load of 162 kN, existing cracks continue to widen and extend, with the width of about 0.8 mm $\sim$ 1.5 mm, and local cracks have extended through the ribbed beams and columns, forming an obvious “X” shape crossing crack in the middle part of the wall. Thus, it can be roughly judged that the ribbed beam and column concrete has cracked and the ribbed beam steel began to yield. The peak load value of this stage of reverse loading is $-$ 129 kN, the cracks continue to widen and form an obvious “X” shape crossing crack, and the cracks on the left edge of the door opening keep increasing. Under a displacement amplitude of 6.7 mm, keep on loading, and the maximum forward load of this stage is 168 kN, and maximum reverse load is $-$ 144 kN. Original cracks go on widening, with all crack width larger than 1 mm, as shown in Fig. 5. Loading under displacement amplitude of 9 mm, this cyclic load can reach to the ultimate load of 172 kN. During the process of loading, the concrete of ribbed beam and column is heard cracking, and intersecting crack is formed in the middle of the wall, with plumped blocks. Loading under displacement amplitude of 12 mm, in the first cycle, the load value is 169 kN, reducing to 97% of ultimate load, the bearing capacity decreases, most steel rebars have yielded, with increasing peeling blocks. At door opening position, it can be observed that the concrete of ribbed beam and column cracks and goes through. For loading in the second cycle, the stiffness degrades seriously, forward load declines to 133 kN, with extended cracks and peeled blocks. When entering the next-stage displacement amplitude of 15 mm, the blocks obviously plump up near the lintel in the middle of the wall and at the top of door opening, the wall surface starts to peel off. At this time, the maximum load is 145 kN, reducing below 85% of ultimate load value. The vast majority of steel rebars have yielded, the wall plumps up and peels off, cracks go through to form evident “X” shape crack, and the wall is damaged. Its failure and crack development are shown in Fig. 5.

Figure 5.

Failure and crack development of specimen MDW-1.

3.2 Test phenomenon of the second group of specimens

Take CDW-1 as an example. Before specimen is loaded, there is no initial crack. When the displacement amplitude rise to 2.7 mm, and the load is 60 kN, the “/” type micro-cracks appear on the first skin block at the lower left corner of the opening. When the displacement amplitude rise to 5.4 mm, and the load is 74 kN, cracks increase at the lower left part of the opening, with extended crack length, and the “/” type diagonal cracks also appear at the upper right corner of the opening. When reverse load is $-$ 80 kN, the “ $\backslash$ ” type micro-cracks start to appear at the upper left and lower right corners of the opening, with crack width of about 0.5 mm. When the displacement amplitude rises to 6.75 mm, load and reverse load are 79 kN and $-$ 89 kN, the oblique micro-cracks increase abruptly at both sides of opening, with concrete cracking sound being heard. The concrete begins to crack, most of which are short cracks, and steel rebars start to yield. Intersecting cracks begin to appear on the left wall of opening, and there are less cracks on the wall right below the opening, as shown in Fig. 6. Loading is added when displacement amplitude reaches to 9 mm and reaches to the maximum at the reverse direction of the first cycle. When the peak load is $-$ 95 kN, the concrete on ribbed beam is heard to crack, most cracks on walls at both side of opening have went through, and the steel rebars of ribbed beam at both sides of opening have yielded greatly. In the second cycle, the stiffness declines to a certain extent. Under reversely loading, the peak load is $-$ 84 kN. Keep on loading, the bearing capacity enters a decaying stage. When the displacement reaches to 12 mm in the first cycle, and the load value is $-$ 94 kN, the concrete of ribbed column at the edge of opening starts to plump, block surface plumps, and the block near the opening starts to peel off. The maximum load in the second cycle is 81 kN, the stiffness degrades slightly. For the displacement of 15 mm and 18 mm in the second cycle, it is loaded until stiffness degradation becomes evidently. Loading to displacement amplitude of 21 mm, the maximum reverse load is 80 kN, the load falls below 85% of the maximum value, the lower blocks at both sides of opening peel off seriously, the concrete of side ribbed column falls off to expose steel rebar. Finally, the bearing capacity continues to decrease, the specimen is damaged, and loading ends. Its failure and crack development are shown in Fig. 6.

Figure 6.

Failure and crack developing of specimen CDW-1.

3.3 Analysis on specimen failure mode

Through the analysis on test phenomenon and referring to research data of related brick wall [4, 6], the failure modes of wall with openings can be roughly divided into: shear compression failure and diagonal-compression failure.

3.3.1 Shear compression failure

From loading to failure, the wall goes through three stages: (1) Elastic stage. At this stage, the displacement-load relation curve basically shows a linear relation, and the stiffness degradation of the wall is less. The wall stiffness is the initial stiffness, until the wall starts to show cracks. (2) Cracking stage. With the increased displacement, the wall begins to show cracks, with quickened stiffness degradation. As cracks just begin to generate, and due to the obstruction of ribbed beam and column, the key failure cracks cannot form immediately. With the continuously increased loads, the cracks become more, expand, extend and gradually go through ribbed beam and column. Then, the concrete cracks, steel rebars start to yield, and stiffness gradually degrades, forming a main crack belt. (3) Failure stage. As the quantity of concrete cracks on ribbed beam and column rises, most steel rebars have already yielded, and bearing capacity enters a decaying stage, stiffness degradation becomes evident gradually. Finally, at the first cycle of certain grade, bearing capacity decreases below 85% of the maximum bearing capacity, and the specimen was damaged.

3.3.2 Diagonal-compression failure

In the diagonal-compression failure process of the wall with openings, the cracking load is about 45% of the peak load. After cracks generate, due to the obstruction of ribbed beam and column, cracks can’t develop continuously with many short cracks, and the location of crack appears as a jumping pattern. Finally, the failure of wall occurs at the intersection of cracks in the middle of the wall, and blocks are crushed. When the wall is crushed, the quantity of cracks on ribbed beam and column is less, and a few steel rebars yield.

Analyzing from the failure phenomenon of six specimens, in the failure process, the blocks crack seriously, the concrete of ribbed beam and column cracks, most steel rebars yield, and finally specimens are damaged. Therefore, the failure mode used for wall specimens with openings are all shear compression failure.

4. Test results and analysis

4.1 Hysteretic behavior

4.1.1 Hysteretic curve

Under the push-pull action of amplitude displacement control, the load-displacement curves of specimens show a recycling ring shape, forming the hysteretic curves composed of multiple hysteretic rings from loading at the beginning to the end. Normal hysteretic curve patterns include: arch, shuttle, S shape and reverse S shape. The hysteretic curves of wall with openings are shown in Fig. 7a–f.

Figure 7.

Hysteretic curve of specimens.

(1) The similarity and difference between hysteretic curves of the first group of specimens

Common characteristics: it can be seen from the hysteretic curves of three specimens that, before the specimens do not crack, the load-displacement curves are basically linear. At the early stage of cracking, stiffness slightly degrades. After unloading, hysteretic ring show a closed form, with smaller area, and the entire hysteretic curve displays a shuttle shape, without showing obvious shear deformation and slippage. As the displacement amplitude increases, bearing capacity rises, the cracking results in increasingly evident stiffness degradation, hysteretic curve slowly becomes full, until reaching to the maximum bearing capacity. When the displacement amplitude is unloaded to zero, the closed phenomenon of hysteretic ring gradually becomes significant. After this, the bearing capacity of specimens enters a declining stage, shear deformation becomes obvious, concrete cracks, and most reinforcement of ribbed beam and column yield. In the second cycles, stiffness degradation expedites, and finally the hysteretic curves of specimens display a reverse S shape.

Difference: as the rate of opening increases, the bearing capacity of specimens shows a decaying trend. In the rising stage of bearing capacity, with the increase of opening rate, stiffness decreases much faster. In the declining stage of bearing capacity, with the increase of opening rate, stiffness decreases much slower, with better ductility, stronger hysteretic energy dissipation capacity and better nonlinear seismic performance.

(2) The similarity and difference between hysteretic curves of the second group of specimens

Common characteristics: in the early non-cracking stage, the load-displacement curves are linear, and the hysteretic ring show a shuttle shape in loading and unloading. As the displacement amplitude rises, the hysteretic curves become more and more full. In the decaying stage of bearing capacity, the hysteretic curves show a closed form after unloading, and finally display a reverse S shape.

Difference: with the increase of opening rate, the bearing capacity of specimens evidently decreases, and so does stiffness. The displacement value of peak load gradually increases, the hysteretic ring becomes fuller, showing better energy dissipation capacity and ductility. After reaching to the peak load, the bearing capacity declines more slowly, and stiffness degradation becomes more slowly.

4.1.2 Skeleton curves

In low cyclic reciprocating loading, connect the corresponding peak load points of displacement amplitude of each stage in the same direction, the skeleton curves of specimens can be obtained, as shown in Fig. 8. Through the skeleton curves of specimens, the yield point, crack point, peak load point, ultimate displacement point and ductility coefficient of specimens can be determined, and the three stages and stiffness degradation that specimens have experienced can also be seen more visually. The skeleton curves of the first group of specimens are shown in Fig. 8a; the skeleton curves of the second group of specimens are shown in Fig. 8b; the skeleton curves of the six specimens are shown in Fig. 8c.

Figure 8.

Skeleton curves of specimens.

It can be seen from the skeleton curve, in the early loading stage, the load-displacement relationship curve is basically linear. With the increase of displacement amplitude, the specimens show cracks. When the stiffness starts to degrade, the curves obviously become bent, and the load continues to increase. As the cracking and deformation rate of wall are expedited, reaching to the maximum bearing capacity, there is evident residual deformation after unloading. Then, as the displacement amplitude increases, the bearing capacity enters a declining stage, the wall cracking aggravates, and stiffness gradually degrades. When bearing capacity reduces to below 85% of the maximum bearing capacity, the specimen is destroyed and loading ends. The specific analysis is as below:

For the first group of specimens, as the opening rate increases, the maximum bearing capacity of specimen shows a declining trend; at the rising stage of bearing capacity, with the increase of opening rate, the stiffness degrades quicker; at the declining stage of bearing capacity, with the increase of opening rate, stiffness degrades slower, ductility is better, hysteretic energy dissipation capacity is stronger, and nonlinear seismic performance is better.

For the second group of specimens, as the opening rate increases, the bearing capacity of specimen decreases, and initial stiffness reduces. At the rising stage of bearing capacity, with the increase of opening rate, the stiffness degrades quicker; at the declining stage of bearing capacity, with the increase of opening rate, stiffness degrades slower, ductility is better, hysteretic energy dissipation capacity is stronger, and nonlinear seismic performance is better.

4.2 Ductility analysis

It is generally known that the greater the stiffness of a structure is, the larger its absorbed seismic force will be, and the worse its deformation and energy dissipation capacity will be [13]. The nonlinear deformation capability and hysteretic energy dissipation capacity of the structure are important basis to determine nonlinear seismic performance. Ductility refers to the inelastic deformation capacity borne by the structure after yielding and before being damaged. When it reaches to the peak load value, the stiffness degradation becomes be slower, deformation keep on increasing, and bearing capacity does not drop rapidly and causes structural damage. This indicates a better ductility.

A structure with large ductility coefficient has good ductility performance. The ductility coefficient is calculated according to the following equation:

$\displaystyle\mu=\frac{x_{u}}{x_{y}}$ (1)

Where, $\mu$ is the ductility coefficient; $x_{u}$ is the ultimate displacement value (the corresponding displacement value when the load value reduces to 85% of the peak load value); $x_{y}$ is the yield displacement.

This test uses the energy method [14] to determine the yield point of specimen. The specific practice is shown in Fig. 9. U point is the peak load point of specimen. Make a horizontal line UY through U point, and then make a diagonal line OY through the origin O to intersect with UY at point Y. When two dash areas OAB and UYB equal, at this time, point Y is the yield point and $\Delta_{y}$ is the displacement value of yield point.

According to the measured skeleton curve data, the eigenvalue point data and ductility factor of each specimen are worked out as shown in Table 4.

Table 4

Summary sheet of test result

Specimen	Opening	Cracking point		Yield point		Peak load point		Ultimate load point		Ductility
no.	rate									coefficient
		Load	Displacement	Load	Displacement	Load	Displacement	Load	Displacement	$\mu$
		/kN	/mm	/kN	/mm	/kN	/mm	/kN	/mm
MDW-1	12.9%	105.00	1.32	150.6	4.66	175.98	8.64	149.58	14.31	3.07
MDW-2	17.3%	68.46	1.35	130.62	4.63	157.93	8.77	134.81	15.00	3.24
MDW-3	21.6%	58.08	1.18	114.83	4.12	140.49	6.77	119.41	14.49	3.51
CDW-1	18.5%	55.36	1.95	78.30	4.74	95.00	8.93	80.75	20.45	4.30
CDW-2	23.1%	30.25	2.09	57.36	5.98	68.00	17.92	57.80	31.88	4.67
CDW-3	27.7%	27.19	1.98	41.55	5.55	49.93	17.79	42.30	31.67	5.06

Figure 9.

Equal energy method.

Comparing the three specimens in the first group in Table 4, with the increase of opening rate, their bearing capacity reduces, the displacement of cracking point reduces, ductility is promoted, energy dissipation capacity is enhanced. Comparing the three specimens in the second group in Table 4, with the increase of opening rate, their bearing capacity reduces, the displacement of ultimate load point increases, ductility is promoted, and energy dissipation capacity is enhanced. Comparing the six specimens in Table 4, with the increase of opening rate, the ductility of specimen shows an increasing trend, as shown in Fig. 10.

Figure 10.

Relation curve of ratio of holes and ductility factor.

4.3 Stiffness degradation analysis

The process that the stiffness of specimen continuously decreases with the increase of displacement amplitude is called stiffness degradation. The paper replaces tangent stiffness with secant stiffness, and the calculation method is as follows:

$\displaystyle K_{i}=\frac{\left|{+{P}_{i}}\right|+\left|{-{P}_{i}}\right|}{% \left|{+\Delta_{i}}\right|+\left|{-\Delta_{i}}\right|}$ (2)

Where, $K_{i}$ is the average secant stiffness of specimens at the $i^{\text{th}}$ cycle; $+P_{i}$ is the peak load value of specimen under the $i^{\text{th}}$ forward loading; $-P_{i}$ is the peak load value of specimen under the $i^{\text{th}}$ reverse loading; $+\Delta_{i}$ is the corresponding displacement value of the peak load value of specimen under the $i^{\text{th}}$ forward loading; $-\Delta_{i}$ is the corresponding displacement value of the peak load value of specimen under the $i^{\text{th}}$ reverse loading.

According to Eq. (2), the stiffness of each specimen is figured out, and its stiffness degradation curves are drawn as shown in Fig. 11.

Figure 11.

Stiffness degradation curves of specimens.

Stiffness degradation analysis:

The stiffness degradation curves of the first groups of specimens can be divided into three stages: rapid stiffness degradation stage at the initial loading period, mitigated stiffness degradation stage and stiffness stabilization stage. Since the specimen is designed according to the size of door opening of actual house (single-door, entry child-mother door, double-door), the size of opening does not differ much. Comparing the three curves, the initial stiffness of specimens before cracking is almost the same. Probably due to the different compactness of fine aggregate concrete, the initial stiffness of MDW-2 is slightly bigger. After the cracking process, the stiffness degradation curves of three specimens show certain law. The stiffness of MDW-1, MDW-2 and MDW-3 reduce successively, so do the stiffness degradation rate. After reaching to the maximum bearing capacity, the stiffness degradation rate of MDW-1 is the quickest. The deformation from the displacement at the maximum load to the ultimate displacement is the smallest, followed by MDW-2. After MDW-3 reaches to the maximum bearing capacity, it has the best nonlinear deformation capacity, slowest stiffness degradation and best ductility.

The stiffness degradation curves of the second group of specimens have three same stages as the first group of specimens. With the increase of rate of hole, the integrity of specimens turns badly, and initial stiffness decreases. In the stable stiffness stage, with the increase of rate of hole, the stiffness declines more moderately. That’s to say, when the curve is more flat, the ultimate displacement will become larger, with lengthened curve and better ductility.

4.4 Analysis of hysteretic energy dissipation

The stronger the structural resistance to inelastic deformation is, the more energy it will absorb in an earthquake, and the better the energy dissipation capacity will be, so the smaller the damage generated will be in the earthquake. Generally, the viscous damping coefficient is used to measure the structural energy dissipation capacity. In this paper, the viscous damping coefficient calculation method proposed by Jacbosno is adopted. The larger the viscous damping coefficient is, the stronger the structural energy dissipation capacity will be, the better the deformation performance will be, and the better the resistance to damage and collapse will be in an earthquake. The specific calculation method is shown in Fig. 12, according to Eq. (3).

$\displaystyle\beta=\frac{1}{2\pi}\times\frac{S(\textit{ABC}+\textit{CDA})}{S(% \textit{OBF}+\textit{ODE})}$ (3)

Where, $S_{(\textit{ABC}+\textit{CDA})}$ is the area of hysteretic ring; $S_{(\textit{OBF}+\textit{ODE})}$ is the sum of the area of OBF and ODE.

Figure 12.

Calculation diagram of equivalent viscous damping coefficient.

Table 5

The equivalent viscous damping coefficients $\beta$ (%)

Specimen no.	Cracking point	Yield point	Peak load point	Failure point
MDW-1	9.21	15.13	21.04	22.55
MDW-2	9.19	15.56	21.54	23.12
MDW-3	9.56	16.37	22.32	24.27
CDW-1	12.36	13.51	15.36	16.07
CDW-2	13.85	14.08	16.85	17.20
CDW-3	14.13	15.40	17.34	17.95

According to above calculation method, the equivalent damping coefficients of all specimen’s characteristic point (cracking point, yield point, peak load point and failure point) are shown in Table 5. It can be seen from Table 5 that, the equivalent damping coefficients of specimens in the group one and two increase with the rise of rate of hole. It indicates that an appropriate opening can enhance the energy dissipation capacity of the component, but the openings should be reinforced. Otherwise, the bearing capacity and stiffness of component will be reduced a lot.

Table 6

Deformation limit of the specimens

Specimen no.	Elastic displacement angle	[ $\theta_{e}$ ]	Elastic-plastic displacement angle	[ $\theta_{p}$ ]
MDW-1	1/1000	1/1000	1/75	1/80
MDW-2	1/900	1/1000	1/75	1/80
MDW-3	1/800	1/1000	1/70	1/80
CDW-1	1/800	1/1000	1/48	1/80
CDW-2	1/600	1/1000	1/42	1/80
CDW-3	1/600	1/1000	1/43	1/80

4.5 Deformation limit of the components

According to the two-stage fortification target required by the current Code for Seismic Design of Buildings in China, the fortification target requirements under the corresponding three performance levels are as follows:

“A minor earthquake without any damage” refers to that in frequent earthquakes, the structure can meet the requirements of elastic-plastic deformation limit and bearing capacity. “A moderate earthquake with repairable structural damage” refers to that the architectural structure has certain plastic deformation capacity and does not generate irreparable destroy. “A strong earthquake without collapsing” refers to that the architectural structure meets the elastic-plastic deformation limit.

According to the test data, the elastic displacement value and elastic-plastic displacement value of each wall can be worked out, and the allowable deformation value of the wall under different performance targets is determined, as shown in Table 6.

5. Conclusions

With the increase of the size of opening, the bearing capacity and stiffness of the wall will be weakened, so it is necessary to take measures to reinforce the opening or limit the size of opening, to ensure neither bearing capacity nor stiffness of the wall would decline too much.

With the increase of door opening and window opening, the wall integrity will weaken, with declining bearing capacity, slower stiffness degradation after yield, larger ultimate displacement, better ductility and enhanced hysteretic energy dissipation capacity. This indicates that, for the walls with larger stiffness, when opening is made in an appropriately way, its seismic performance can be improved under no significant decrease of bearing capacity.

According the test data, the elastic displacement value and elastic-plastic displacement value of each wall is worked out, so as to determine the deformation limit of walls at different performance objective.

Footnotes

Acknowledgments

This work was support by the National Natural Science Foundation of China (No. 51578253); Scientific and Technological Planning Project of Xiamen City (No. 3502Z20172011 and 3502Z20172014); Scientific and Technological Planning Project of Quanzhou City (No. 2018C083R); Reform study of graduate education and teaching of Huaqiao University in 2018 (No. 18YJG55).

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Seismic behavior of energy-saving block & invisible multi-ribbed frame walls with different sizes of openings

Abstract

Keywords

1. Introduction

2. Test profile

2.1 Specimen design and reinforcement

Table 1 Mechanical properties of steel reinforcement

2.3 Lading set-up and loading process

3.1 Test phenomenon of the first group of specimens

3.3.1 Shear compression failure

3.3.2 Diagonal-compression failure

4. Test results and analysis

4.1 Hysteretic behavior

4.1.1 Hysteretic curve

(1) The similarity and difference between hysteretic curves of the first group of specimens

(2) The similarity and difference between hysteretic curves of the second group of specimens

5. Conclusions

Footnotes

Acknowledgments

References

Table 1
Mechanical properties of steel reinforcement