An Overview on Parametric analysis of knee bracing on the seismic behavior of steel moment frames using pushover analysis

Hossein Lotfi*1

1- M.sc of Marine Structures Engineering, Tehran Polytechnic University, Corresponding author: (Hoseinlotfi@aut.ac.ir)

Abstract

The present research aims to shed lights on the seismic behavior of frames with knee bracing systems. To this end, the design of frames with different number of 3, 5 and 7 story was modeled based on Regulation 2800-Fourth Edition and the Code 360 and using SAP2000 software. Then, the seismic behavior of the modeled frames with knee bracing system with different dimensions and positions of the knee element was measured under pushover analysis. Finally, the seismic parameters of the system of braced structures with knee braces were presented in the form of diagrams and tables and then they were compared with each other and the results are presented. Given the results, the seismic behavior of KBF system in frames with different story and in different situations of dimensions and position of diagonal and knee elements, by achieving maximum ductility and stiffness and finally the highest coefficient of behavior of frames has the most optimal design. The results also showed that in this lateral bearing system, the diagonal member passes through the beam-column joints and halves the knee member, which determines the stiffness of the system diagonal member. While the ductility of the system is obtained from the flow of the knee member and acts as a ductile fuse and prevents the reduction of the diagonal member.

Keywords: Seismic behavior, Braced frame, Knee brace, Pushover analysis, Behavior coefficient

1-Introduction

While designing structures, two important factors should be taken into account, first, the structure must be stiff enough to control lateral displacement, to prevent structural and non-structural damage. Second, it must have good formability, to prevent sudden breakdown. Considering that the issue of energy consumption in structures under strong earthquake forces has attracted a lot of attention [1]. Each of the common structural systems in the process of dealing with lateral forces in the linear and nonlinear region has advantages and disadvantages. For example, the moment resisting frame (MRF) is an architecturally suitable system due to its significant free distance between columns for the installation of openings, and has a relatively good ductility and energy dissipation capability; However, due to low lateral stiffness, it shows a large horizontal displacement in front of the lateral forces and therefore suffers greatly from the P-Δ effect, which changes the economics of this system compared to other systems. On the other hand, the conventional Concentric Braced Frame (CBF) has a very high lateral stiffness and is an economic system because in this system, the lateral forces are transmitted axially by the members. However, this system does not have proper ductility and energy dissipation due to buckling of the braces against pressure. Therefore, it can be said that these two systems, each alone, cannot provide both stiffness and ductility in an optimal way, and the provision of both goals by these systems makes the design uneconomical [1].

Due to the mentioned problems in recent years, researchers' efforts to simultaneously achieve the three parameters of the above structures, has led to the introduction of new systems such as off-axis bracing system (EBF) and knee bracing system (KBF). Off-axis bracing system, in addition

to having high stiffness in the linear region, if the special criteria are observed, has a good ductility and is considered an economic system [2]. Despite the many advantages of this system, it has some disadvantages, such as excessive distortion of the roof due to excessive deformation of the connecting beams. Also, because in this bracing system, the connecting beams, as formable elements and energy consuming system, are part of the main members of the structure (beams), so the possibility of quick and low cost replacement of these members in order to reuse There is no structure [3]. Another system that has been introduced recently and in addition to having the advantages of off-axis bracing system, does not have the mentioned problems, is the knee bracing system. This system, introduced by Belandra et al. (1990) at the University of Singapore [4], is in fact a modification of another system called the interchangeable knee bracing system (DKB), previously proposed by Ochoa (1986). Ochoa suggested that the non-linear member in this system be designed in such a way that it can only withstand tension and that both the stiffness and ductility factors can be provided by the knee member [2]. In the knee bracing system, the end of the diagonal braces is attached to an inclined element attached to the beam and column or column and column and abutment, instead of connecting to the intersection of the beam and column. This element, which is known as the knee member, as a malleable element of the system, by deforming its plastic, causes energy dissipation during the occurrence of severe earthquakes [5]. The noteworthy point in this bracing system is that after the end of the earthquake, only its knee member is damaged and surrenders and the main frame of the diagonal braces remains elastic. In this case, only with easy and low cost replacement of the knee member, the structure has the ability to be reused [6].

After the introduction of the knee bracing system, a lot of research has been done on the use of this system in structures, and this research continues today. Among the researches in this field, we can study the study of Zhen et al. [7] regarding the inelastic analysis of knee braces, Mofid and Lotfollahi [8] in relation to the nonlinear behavior of knee braces under lateral loads in flexural and shear yield modes. The study of Okazaki et al. [9] on the performance of grafted beams in earthquake-resistant divergent braced frames under intermittent loading, Richard and Yang study [10] on the effect of width-to-thickness ratio on the performance of grafted beams in knee braces, Zahraei and Jalali [11] for analytical and laboratory analysis indicated the degree of viscosity damping equivalent to the inelastic behavior of braced knee frames. In-house research has been done in the field of this bracing system, among which we can use Ghodrati Amiri and Naeemi research [12] to investigate the seismic performance of frames with knee braces in comparison with cross braces, Zahraei and Masjediri [13] To study the lateral behavior of structures with knee braces, Haj Mohammadi et al. [14] In order to use knee braces simultaneously in frames with divergent braces, eccentric with vertical link and knee braces, Kardan Gharamaleki et al. [15] Regarding the ability of knee braces to improve and reduce the seismic needs of concrete bending structures, Aghayari and Vaziri research [16] in order to achieve proper ductility and no buckling in the nonlinear behavior of knee braces, Azar and Jafari [17] research on evaluation parameters affecting the behavior of knee braces in steel structures, Dizangian and Taghavi research [18] on the performance of malleable knee elements in the multi-storey bracing system of high-rise buildings with perimeter frames and Dolati study [19] on evaluating the strength of steel frames with types م Knee bracing for progressive failure using nonlinear static alternative path analysis. Given the fact that research in the field of knee bracing systems is limited, so in the present article we tried to investigate the seismic performance of steel frames with knee bracing system using pushover analysis method.

2- Methodology

This research includes analytical and simulation with SAP2000 finite element software to design steel frames and investigate the performance and seismic behavior of the knee bracing system in this type of frames. For this purpose, the behavior of this bracing system with different dimensions and different placement positions in steel frames with short to medium grades was investigated. Hardness and finally the appropriate behavior coefficient were determined.

In addition, in this study, the parametric study of knee brace members was performed and by changing the knee member and changing the length of the diagonal member to the knee member, the coefficient of frame behavior in different joint positions (rigid, semi-rigid, articulated) and in terms of position Geometric placement was examined to achieve proper stiffness and ductility. After reaching the optimal position of the knee element, the analysis of different models with the number of short to medium story has been done. It should be noted that in order to design and model the frames in this study, pushover nonlinear static analysis was used and their seismic loading was used using 2800 [20] and AISC ASD89 [21] and FEMA356 [22] Was evaluated.

Progressive nonlinear static analysis or pushover analysis is a method for determining the additional strength and ductility and the formation of plastic joints as well as the formation of the mechanism of destruction of structures. In this method, the lateral force of the earthquake is simulated by the static force that affects the story of the building and the pattern of distribution of these forces is the same inertial force created in the position of significant masses of each story during an earthquake. These forces increase until they reach the final load or displacement of the target. In this case, the performance behavior of the structure can be evaluated [23]. In general, the pushover analysis method is not based on specific theoretical principles and is based on the principle that the response of the structure can be simulated by the response of the system of one degree of freedom with equivalent characteristics. This assumption leads that the response of the structure depends only on one deformation mode (the shape of the first vibration mode) and its shape remains constant during the analysis. Although both of these assumptions may seem inaccurate, extensive research over the past few decades has shown that for structures in which the first oscillation mode is predominant, good estimates of the system's maximum reflections to the help of this analysis is obtained [24].

1.2. Modeling frames

The sections of the frames studied in this research were first modeled and designed according to AISC regulations (ASD89) and using SAP2000 software, and then the initial and actual sections were designed and considered for them and the dough joints were assigned to the members. Due to the existence of different parameters in an analytical model that are variable, some specifications in the models, including consumables and the length and number of openings and loads on the structures and the height of the fixed story have been considered. The modeled frames were then evaluated under nonlinear static analysis and after performing the analysis process in three dimensions in SAP2000 software, the analysis steps in the software continued until it led to instability in the desired frame of the type Create a soft story or high ductility in the structure; Otherwise, the modeling assumptions and the initial design were slightly changed and the previous process was repeated to create the mentioned instability. For this purpose, first by modeling frames with knee braces with 3, 5 and 7 story, the seismic behavior of these frames has been studied under pushover analysis and then to determine the parametric effect of the knee member on the coefficient of behavior of the structure under pushover analysis. , The mentioned frames, the obtained results have been evaluated.

The design of the frames studied in this research is based on the forces resulting from gravitational and seismic loads and also in choosing the plan, the length of the openings is in

accordance with the common buildings. For this purpose, a regular plan with dimensions of 20 x 20 and four openings of 5 meters in each direction was considered. Then, the modeled structures were examined under the effect of equivalent static analysis in accordance with the loading regulations of Iranian Standard 2800. Table 1 presents the specifications of the selected structures as well as the various parameters related to the models. To calculate the rotation period of the frames, the experimental relations in standard 2800 according to equation 1 for medium moment frame steel structures have been used.

(1) T = 0.05 H3 / 4

In Table 2, the required seismic parameter values are calculated and based on the T parameters of the periodicity of the structure, B is the reflection coefficient and C is the earthquake coefficient. Thus, the values required for static analysis equivalent to the frames were calculated and then the frames were calculated and designed under this type of analysis so that the members used in these frames are normal.

Table 1- Loading and analysis specifications in modeled frames

Table 2 - Parameters related to modeling frames with knee braces with different

number of story 581 Kg/m Dead load story

For all frames

200 Kg/m Live load story

531 Kg/m Dead roof

150 Kg/m Live roof

688 Kg/m Side wall load A=0.35

3m Story to story height I=1

3m Pilot story to story height R=7

C B T(sec) story model 0.1250 2.5 0.436 3 3

story 0.1060 2.5 0.5 5 5

story 0.0839 2.11 0.6435 7 7

story

In order to design the frames studied in this research, according to the standard 2800-fourth edition, in the modeling, the location of the center of stiffness has changed by changing the location of the braces. It should be noted that in the frames, the coordinates of the center of mass and the center of gravity are equal to x = 10 and y = 10. Figure 1 shows the three-dimensional view of the frames with the number of different story modeled in order to conduct this research.

Thus, the frames were modeled and designed with different number of story, and to perform the design operation, standard 2800 clauses were observed and a combination of 30-100% loads was applied on the frames. Finally, the structural drifts were checked so that they did not exceed the allowable values. It should be noted that in the knee brace system, the main members of the frame, or beams and columns, are designed in such a way that they remain in the elastic range and their instability is prevented and the diagonal element does not buckle, observing the rules of the regulations. Create a knee. To explain the naming of sections, it should be said that box sections are used for columns, the first number indicates the side of the box and the second number indicates the thickness of the sheet. For beams, normal beams and double sections have been used. Double stud sections were used for bracing and box sections were used for knee members.

3 story frame 5 story frame 7 story frame

Figure 1- Sample of modeled frames with different number of story

2.2. Selective layout model in knee brace

Due to the existence of different parameters in the models studied in the present study and how knee bracing works as a member of the structure to withstand lateral loads, the use of optimal model in analysis and design is very important and its impact on research results is inevitable. Is. Therefore, in the present article, four types of models with different arrangement and arrangement of knee braces according to Figure 2 have been used with each other and by comparing the results of analysis related to each of these arrangements, the shortcomings of each were shown.

Considering the geometry of the knee brace, it can be expected that the knee brace in model 2 will be tensile and compressive and the structure will have a more acceptable performance against the lateral force than model 1. However, the distance from the center of mass to the center of gravity is an important factor in how the structure works against lateral forces, and the greater the distance, the better the performance of the structure; Accordingly, by changing the geometry of the knee brace to create a greater distance from the center of gravity to the center of mass, the Model 3 can have a better performance than the Model 2, but no matter how much the structure overturns depending on the reaction force of the columns , Less, the structure will perform better against lateral forces, so if we compare shear force of the columns of a structure, due to the higher axial force that the middle columns bear than the side columns. Therefore, the amount of force on the action of the middle columns is much less than the side columns, so if the knee brace is attached to the middle columns when lateral force is applied, the structure will have a more suitable function Model 4 will be the model of choice for further discussion.

Model N.1 Model N.2 Model N.3 Model N.4

Figure 2- Models of knee brace arrangement in the studied frames

According to the recommendations mentioned in previous studies, beam and column sections, diagonal member and knee element were selected and member sections after loading were designed according to AISC regulations (ACD89). The design of these frames under design loads is such that the beams and columns are in the elastic range and the diagonal member does not buckle, and in the design of the knee member, the general, local and lateral torsional buckling constraints are observed.

3. Results of numerical analysis

1.3. Move the target

Various methods have been proposed to determine the target displacement, and the coefficient method has been used here. This method was first proposed by Krawinkler of Stanford University in 1996 and later incorporated into FEMA-273 by the American Council on Applied Technology (ATC). In this method, the target displacement is obtained by multiplying the elastic spectral displacement by the first period of vibration of the building in a set of different coefficients that represent 4 factors (1) the ratio of spectral displacement to roof displacement, (2) displacement ratio Elastic to non-elastic displacement, (3) the effects of deformation-related hysteresis on the displacement response of the structure, and (4) the effects of dynamic phenomena on the displacement response. According to this method, the target displacement in the frames modeled in this part of Equation 2 was calculated using the hypotheses and tables in the Code 360.

2

0 1 2 3 24e

t a

TC C C C S

πδ =

Table 3: Pushover analysis parameters

story 0C 1C 2C 3C T (cm) tδ 3 1.3 1.34 1.05 1 0.341 4.62 5 1.4 1 1.1 1 0.500 8.38 7 1.46 1 1.1 1 0.644 12.23

Thus, the amount of target displacement was calculated for the studied frames, but to reach the nonlinear stage, 1.5 times the value of the software was entered. Then the parameters of plastic joints were introduced to the software. FEMA356 was used to determine the parameters related to plastic joints. Thus, for the columns, automatic plastic joints of P-MM type were used at the beginning and end of the column, and for the beams, automatic joints of type M3 were used in the middle of the beam. And the end was used. But for bracing members, because the sections were made manually with the help of Section Designer, the software does not have the ability to assign automatic plastic joints to these sections. Therefore, calculations were performed for these members according to the mentioned tables and the parameters related to them were assigned as described in Table 4. Admission criteria were calculated according to the tables listed in Table 5.

Table 4: Parameters related to plastic joints of bracing members

Section A(cm2) Fa(Kg/cm2) Pc(Kg) ∆c(cm) Pt(Kg) ∆t(cm)

2���10 26.92 557 19894.10 0.18 71068.80 0.65

2���12 33.96 554 24938.14 0.18 89654.40 0.65

2���14 40.8 601 32898.12 0.20 107712.00 0.65

2���16 48.15 667 43826.63 0.22 127116.00 0.65

2���18 56.08 772 60782.14 0.27 148051.20 0.65

2���20 64.6 813 74568.44 0.29 170544.00 0.65

2���22 75.1 847 91160.51 0.30 198264.00 0.65

2���24 84.86 879.5 107863.32 0.31 224030.40 0.65

Table 5: Acceptance criteria for knee bracing performance levels

criteria ¤

Immediate Ocupancy (IO) 0.25 -0.25

Life Safety (LS) 7 -4

Collapse Prevention (CP) 9 -6

In this way, the modeled frames were subjected to pushover analysis and the results were examined, which are described below. In addition to analyzing and designing frames with knee braces, to study the parametric effect of the knee member on the seismic behavior of structures and determine the coefficient of behavior of structures with different number of models, modeling another number of frames according to the following conditions and their results Is located.

2.3. Plastic joints formed in the frames

After pushover analysis, plastic joints were formed in the structural members. Here, from the total loading modes, the most critical mode was selected, which is presented in Figure 3, the results related to the plastic joints formed in the frames of 3, 5 and 7 story, respectively. By comparing the joints formed in the frames, it is clear that the formation of joints has a relatively regular process and more joints are formed in the knee joints, which is the designer's intention, and in general the reason for using this bracing system is the transfer of damage from diagonal members to knee members.

3����� ����� 5����� ����� 7����� �����

Figure 3: Plastic joints formed in the studied steel frames

3.3. Pushover curve

Figure 4 shows the most critical pushover curve for all models. It should be noted that the unit of sheer force of the body and the unit of displacement in the diagrams is centimeters. Observing the pushover curves of frames with different number of story, it is observed that with increasing the height of the structure, more shear force was required to change the target position in the structure, and in longer frames, more force is required for this purpose.

Figure 4: Pushover curve of the studied frames

4.3. Ductility coefficient

To calculate the ductility coefficient (Rw) of the existing frames, the relations presented in Chapter 3 were used and the ductility coefficient obtained for different frames modeled with different number of tiers is shown in Table 6. Observing the calculated coefficient of behavior for frames with knee braces with different number of layers, we reach approximately 6.95 which is a logical number for the ductility of frames with knee braces and it is also observed that with increasing the number of frames, the amount Ductility is decreasing. The following are the results Each part of the models is presented and reviewed.

Table 6: Parameters of ductility coefficient of frames with different number of layers

frame ∆y(cm) ∆u(cm) Vy(ton) Vs(ton) Ru Rw

3 3.5 7 560 210 5.53 7.96

5 6.6 13 660 320 4.83 6.95

7 12.3 19 910 445 4.69 6.76

4. Investigation of the effect of frame members on the behavior of knee bracing system (KBF)

1.4. The effect of connecting the knee element to the beam and column on the lateral displacement of the frame

Figure 5 shows the comparative results related to the effect of the type of knee connection in the KBF bracing system to the beam and column on the lateral displacement of the 3-story frame. According to the figure, it can be seen that the amount of lateral displacement of the frame in different classes by changing the way the knee element is connected to the beam and column is different from the clamped to the semi-clamped and articulated position. Therefore, it can be concluded that the displacement of the frame story is less when a single knee element is used than when a double knee element is used, and therefore the use of a single brace is more appropriate.

Figure 5: Comparison of lateral displacement of the frame between the two modes of using double and single knee elements

2.4. The effect of how the diagonal member is connected to the lateral displacement of the frame story

Figure 6 shows the results related to the effect of how the diagonal member is connected to the lateral displacement of the 3-story frame story. A comparison of the displacement between the two states of connection of the diagonal member to the knee member in the case of two articulated heads and two clamped heads and the connection of the knee element to the beam and column in three articulated and semi-clamped and clamped states. If the head is stuck, the difference in displacement between the two is almost negligible.

Figure 6: Comparison between the connection of a diagonal knee to a knee knee in the case of a joint with two joint ends and two clamped ends

3.4. Investigation of the stiffness of the frame story in different connections of the knee element to the beam and column

The amount of frame stiffness in different classes is different by changing the type of single-beam element connection to beams and columns in three modes of double-sided and double-sided connection and two-joint connection, which are shown in Figure 7. 7 story are shown at different knee joints.

Figure 7: The stiffness of the story in the various joints of the knee

4.4. Comparison of stiffness of story in single and double knee modes for different connection modes

Figure 8 shows the results of comparing the stiffness of the story in two single and double knee modes for different connection modes. Comparison of the results related to the stiffness of the story in single and double knee modes for the 3-story frame shows that when a single knee with a rigid beam-column connection is used, the stiffness is higher than the other modes. The degree of stiffness in the case of a double knee used for the bracing system is approximately equal to the stiffness in the case of a double-headed beam connection in the case of a single knee with a semi-rigid connection.

Figure 8: Comparison of stiffness of story in single and double knees for different connection modes in a 3-story frame

5.4. Investigating the effect of knee connection type on story stiffness

Figure 9 shows the results of the study of the effect of the type of knee joint connection on the stiffness of the story. In the connection of the knee to the beam and the connection of the knee to the column, it can be seen according to the following figure, a comparison of the type of rigid and articulated connection of this connection and it was concluded that the connection of the knee to the beam , Will not make much difference in the stiffness of the frame.

Figure 9: Comparison of the type of rigid and articulated connection of the knee element to the beam and column on the stiffness of the 3-story frame

5. Investigating the effect of changing the characteristics of the knee element on the coefficient of behavior of the frames

1.5. The effect of changing the junction of the diagonal and knee members on the coefficient of behavior of the frames

In this section, the results related to the effect of changing the characteristics of the knee element on the coefficient of behavior of the frames are studied. For this purpose, considering three factors, namely (1) change the junction of the diagonal and knee member, (2) change the position of the knee element to the diagonal member, and (3) change the length of the knee element and also (4) compare the effect of different cases h / b and h / H together, the effect of these changes on the coefficient of behavior of the frames has been studied. It should also be noted that in the results presented below, the meaning of different joints is ، rigid, semi-rigid and articulated joints, knee to beam and column; The lengths H, h, B, b, L1 and LKnee in an knee bracing system are also shown in Figure 10.

Considering that the results of this section follow a special trend for frames with different number of story, for this purpose, the results related to the coefficient of behavior of a 7-story frame with knee brace have been evaluated taking into account the mentioned different cases. The same process results for the 3rd and 5th story frames, details of its calculations have been omitted. In other words, by changing the different states of the position of the knee element and its geometry, the maximum value of the coefficient of behavior of the 7-story frame for different values of h / H, h / b and L1 / LKnee is determined as the optimal values.

Figure 10: Geometric members and dimensions used in a frame with an knee brace system

By changing the position of the knee element, ie changing the value of the h / b ratio from 0.4 to 0.8 with a step of 0.1, and also changing the length of the diameter of the diagonal member to the knee member, ie changing the L1 / LKnee ratio from 0.3 to 0.7 with Step 0.1, the coefficient of behavior of the 7-story frame was calculated for different states of the h / H ratio from 0.2 to 0.4. It should be noted that L1 is the distance between the knee-diameter joint and the knee-beam joint, and LKnee is the length of the knee element.

Table 7: The effect of changing the junction of the diagonal and knee members on the behavior coefficient of the 7-story frame

h/H=0.2 H/B=0.4 h/b=0.5 h/b=0.6 h/b=0.7 h/b=0.8 knee/L1L R1 R2 R3 R4 R5

0.3 6.3 6.2 5.65 6.6 5.24 0.4 6.6 7 7 7 7 0.5 7 7.6 7.35 7.4 7.2 0.6 6.5 6.5 6.94 6.75 6.9 0.7 5.5 5.5 5.3 6 6.5

h/H=0.3 H/B=0.4 h/b=0.5 h/b=0.6 h/b=0.7 h/b=0.8 L1/Lknee R1 R2 R3 R4 R5

0.3 5.5 6.2 5.8 5.75 5.9 0.4 5.3 6.5 6 6.25 6 0.5 6.6 7 7.2 7 6.6 0.6 6.5 6.6 7.4 5 5.4 0.7 5.7 6 4.9 5.2 5.5

h/H=0.4 H/B=0.4 h/b=0.5 h/b=0.6 h/b=0.7 h/b=0.8 L1/Lknee R1 R2 R3 R4 R5

0.3 6.3 5.8 5.7 5.95 5.65 0.4 6.6 5.9 5.4 6.24 6 0.5 6.5 6.5 6.4 6.5 6.2 0.6 6.4 5.6 6 5.6 5 0.7 6 5.5 5.5 6.2 4.9

Figure 11: The effect of changing the junction of diagonal and knee members on the coefficient of behavior of the 7-story frame

According to the above diagrams, it can be seen that when L1 / LKnee approaches 0.5, the structure has the highest coefficient of behavior. That is, when the diagonal member crosses the middle of the knee, the frame has the most ductility. In all cases, the H / B value is constant and equal to 0.6; As a result, in the case where the value of the ratio (h / b) / (H / B) is approximately equal to 1, it can be concluded that the value of ductility is close to its maximum. That is, the diagonal member passes through the middle of the knee joint and through the collision of the beam and the column, and is parallel to the hypothetical diameter of the frame.

According to the above diagrams, for proper ductility and lateral stiffness, it should be L1 = L1 / LKnee 0.5 and the direction of the diagonal member passes through the beam and column collision, and finally L1 / LKnee> 0.6 is recommended for the appropriate behavior coefficient. Becomes.

2.5. Effects of changing the position of the knee element to the diagonal member on the coefficient of behavior of the frames

In the previous section, it was concluded that if the direction of the knee member is parallel to the hypothetical diameter of the frame and the diagonal direction passes through the intersection of the beam and the column, it is the most suitable case for the ductility of the structure. In this section, the amount of h / b is equal to 0.4 to 0.8 with a step of 0.1 for three modes of h / H equal to 0.2, 0.3 and 0.4. The results show that when the value of h / H ratio is equal to 0.2 and 0.3, the value of the coefficient of behavior has its maximum value which is 0.5 h / b, especially when h / H is equal to 0.2, the optimal state of behavior coefficient R is observed in the structure. Also, when the value of the h / H ratio is 0.4, the numerical value of the behavior coefficient is not a function of a definite state and it is not possible to express a specific range for the optimal state of the h / b ratio.

Table 8: The effect of the position of the knee element to the diagonal member on the coefficient of behavior of the 7-story frame

0.5=Knee/L1L h/H=0.2 h/H=0.3 h/H=0.4 h/b R1 R2 R3 0.4 7 6.1 6.75 0.5 7.6 7 6.5 0.6 7.4 7.1 6.4 0.7 7.35 7 6.5

44.5

55.5

66.5

77.5

8

0.2 0.3 0.4 0.5 0.6 0.7 0.8

R

L1/LKnee

h/H=0.2

h/b=0.4

h/b=0.5

h/b=0.6

h/b=0.7

h/b=0.84

5

6

7

8

0.2 0.3 0.4 0.5 0.6 0.7 0.8

R

L1/LKnee

h/H=0.3

h/b=0.4

h/b=0.5

h/b=0.6

h/b=0.7

h/b=0.8

0.8 7.2 6.2 6.2

Figure 12: The effect of the position of the knee element to the diagonal member on the coefficient of behavior of the 7-story frame

3.5. Effect of knee element length changes on frame behavior coefficient

According to previous measurements, if the optimal geometry is equal to 1 (h / b) / (H / B), that is, if the ratio h / b of the angle that the knee element makes with the beam is assumed to be constant, the length of the knee element is a function of h / H will be. In the analysis, the value of <35 / h / H> 0.2 should be considered, because if the value of the ratio is <0.2 / h / H, the knee element becomes flexible and if its value is <0.35 h / H, the elastic stiffness is greatly reduced and the expectations from the knee brace will not be met.

Table 9: The effect of changes in the length of the knee element on the coefficient of behavior of the 7-story frame

0.5=Knee/L1L h/b=0.4 h/b=0.5 h/b=0.6 h/b=0.7 h/b=0.8 h/H R1 R2 R3 R3 R3 0.2 7 7.6 7.35 7.4 7.2 0.3 6.6 7 7.2 7 6.6 0.4 6.5 6.5 6.4 6.5 6.2

4

5

6

7

8

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

R

h/b

L1/LKnee=0.5

h/H=0.2

h/H=0.3

h/H=0.4

4

5

6

7

8

0.1 0.2 0.3 0.4 0.5

R

h/H

L1/LKnee=0.5

h/b=0.4

h/b=0.5

h/b=0.6

h/b=0.7

h/b=0.8

Figure 13: The effect of changes in the length of the knee element on the coefficient of behavior of the 7-story frame

As can be seen from the table and figure above, the behavior coefficient (R) decreases with increasing h / H ratio in different cases of h / b. If it is <0. h / H, the elastic stiffness increases but the ductility decreases, ie the main members of the beam and column submit faster at the knee joint, and if it is considered <0.4 h / H, it bends to the frame. As we get closer, the ductility increases and the knee joint breaks down very quickly without damaging the beam and column at the joint. Therefore, in the design, it is suggested that the knee elements be considered for 0.35 h / H> 0.2 so that both ductility and elastic stiffness are acceptable. Also, according to the above figure, it can be seen that the coefficient of behavior when h / H is equal to 0.2 in h / b is equal to 0.5 more than other cases and when h / H is equal to 0.3. In the case of h / b, it is equal to 0.6 more than the other cases. The coefficient of behavior when h / H is equal to 0.4 in the case of h / b is equal to 0.5 and 0.6 is almost equal to each other and is higher than other cases. Comparison of different states of h / b shows that the behavior coefficient decreases with increasing h / H ratio. Therefore, the mode h / H equal to 0.2 can be considered more suitable than other modes for design and the appropriate range for h / b can be considered 0.6 <h / b <0.5.

4.5. Determining the coefficient of behavior in 3rd and 5th floor frames

According to the results obtained for the 7-story frame, when the position of the knee element was in the values of h / H = 0.2, h / b = 0.5 and L1 / LKnee = 0.5, the frame had the highest coefficient of behavior. Therefore, the above values are considered as the optimal values of the position of the knee element and the results of the coefficient of behavior are generalized for frames 3 and 5 and for each frame, the coefficient of behavior is according to Table 10. Based on the results, it can be seen that the coefficient of behavior increases with increasing elevation.

Table 10: Optimal behavior coefficient in different frames of 3, 5 and 7 floors

h/H=0.2 h/b=0.5 0.5=Knee/L1L Behaviour coeficient

μ Ω Y R بقاتط3 2.2 1.8 1.44 5.7 5 2.4 1.83 1.44 6.32 7 2.6 1.86 1.44 7

7. Conclusion

The results of the formation of plastic joints in frames with knee bracing system show that the formation of these joints has a relatively regular process and are mostly formed in the knee joints, which is desirable and considered by the designer and such an behavior occurs during an earthquake. In the bracing system it would be logical.

Observing the pushover curves of frames with different number of floors, it is observed that with increasing the height of the structure, more shear force was required to change the target position in the structure, and in longer frames, more force is required for this purpose.

Observing the calculated coefficient of behavior for frames with knee braces with different number of layers, we reach approximately 6.95 which is a logical number for the ductility of frames with knee braces and it is also observed that with increasing the number of frames, the amount of shape Flexibility is decreasing.

The results show that when using a frame with a single knee, in all the different positions of the joint, less displacement is observed than the double knee position, and this means that the stiffness of the frame is greater in the single knee position, which indicates the use of a single knee. Single is more appropriate.

The results show that the type of diagonal connection to the knee, which can be rigid, semi-rigid and articulated, does not have a significant effect on the stiffness of the floors. Also, the stiffness of the floors is more sensitive to the type of knee connection to the beam and column, in frames with lower height.

If the diagonal connection to the knee joint (which is common) is the case where the knee joint to the beam is rigid and the knee joint to the articulated column is more rigid than the case where the knee joint to the beam is rigid and the knee joint to the column is rigid. Be.

The results of changing the position and geometric characteristics of the knee brace system show that in the case where the ratio is 0.2 h / H, with increasing the ratio h / b, the behavior coefficient R of the frame decreases. The results also show that in the case where the ratio is 0.2 h / H and the ratio is 0.5 / h / b, the diagonal and knee joint has little effect on the coefficient of behavior of the frame. In addition, if the ratio is h4 / H = 0.4 and the ratio is h / b = 0.4, the diagonal and knee joints have little effect on the frame behavior coefficient.

If in a knee brace system, a diagonal member is attached to the center of the knee element, the coefficient of behavior decreases as the knee length increases. However, if the diagonal member is connected to the center of the knee element and the knee joint to the column is a fixed point, if the knee angle with the column increases, the coefficient of behavior increases first and then decreases, and can be said to be approximately The ratio of 0.5 = h / b, the coefficient of behavior has its maximum value that can be recommended for design.

If the knee connection to the beam and column is rigid, the stiffness and ductility of the frame is greater than in cases where the connection is semi-rigid or articulated. The results also show that with increasing the number of structural floors, the coefficient of behavior of the structure increases.

8- Reference

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