Calculating the rigid frame diagonal strut for Multi-ribbed composite wall

Abstract

Multi-ribbed wall plate with lightweight frame structure is a new structural system that the weight is light, the rigidity is big, the anti-seismic capacity and the effect of saving energy are good, the social benefit is high, green and environment protection, which different from structure of ordinary frame and shear wall. Multi-ribbed composite wall is the main components of Multi-ribbed wall plate with lightweight frame structure. In this paper, the calculating model of rigid frame with diagonal strut for Multi-ribbed composite wall was discussed. In order to calculate the Multi-ribbed composite wall conform to the rigid frame diagonal strut model, the entity model and the rigid frame diagonal strut model of Multi-ribbed composite wall were built under the same condition of materials and specimens size to calculate monotonic loading condition, at the same time, the mechanical properties and deformation situation of the Multi-ribbed composite wall at work were analyzed. The diagonal strut width was determined by the Mechanics theory to establish the entity model and the rigid frame diagonal strut model, and comparing the stress and strain of the entity model and the rigid frame diagonal strut model about Multi-ribbed composite wall to prove the rigid frame diagonal strut model Suitable for solve the Multi-ribbed composite wall to provide the theoretical basis.

Keywords

Multi-ribbed composite wall the entity mode rigid frame diagonal strut model non-linear finite element

1. Introduction

In recent years, the sustaining rapid development of China’s economy has promoted the pace of urbanization, and the demand for architecture has been increasing. The architecture not only to meet the material needs, but also to meet the requirements of spiritual civilization. The per capital residential area from the original 18 square meters to the present 27 square meters, and the growth rate of up to 50%. Although the urban residential construction area rose linearly, the construction area still can not meet the market needs, so the housing construction is facing unprecedented challenges; therefore, the housing industry came into being, and the residential industry as an important part of China’s national economy. Through the basic and related policy research and the using of high-tech to promote the modernization of the housing industry for meet the growing needs of the people, and which accelerate the modernization process of China’s housing industry so as to improve people’s life quality, and it is the best way to improve the life quality.

Developed countries in the world through the implementation of housing industry modernization to accelerate development the housing residential construction and led the relevant industries and the entire social-economic development. Since the reform and opening up, China’s housing construction continued high-speed development, and the housing industry has become China’s national economic development pillar industry and new growth point. Looking back at history. Since the 1970s, the construction department vigorously carry out wall reform and gradually promote a variety of hollow brick, porous brick, non-clay brick and block instead of clay brick, because clay brick production can be local materials, but the destruction of farmland, energy consumption and brick wall seismic performance is poor. China’s housing construction is still in the extensive production stage, and residential structure is a single form. The construction industry is poor, and labor productivity and technical content are low, so energy and raw material consumption are large. Today, China’s annual construction of various buildings nearly one billion square meters, and it need to use a large number of wall materials. Because of China’s large population and energy shortage, the development of lightweight high-strength, energy-saving earthquake, the use of “three wastes”, green, saving land, reduce costs and there is a certain level building production of industrial structure as the new system is imperative.

Into the 21st century, China’s urban demand for high-rise residential buildings will increase year by year with the tension of urban land; however, there are still few forms of residential structures can be applied to high-rise buildings so far. The advantages of the frame structure is more flexible layout and generally meet the user requirements of the opening and closing, and the frame structure have good ductility, but the frame structure is a flexible structure, and the frame structure the lateral stiffness is small, so it is difficult to meet the requirements of more than 10 structural deformation. In addition, the frame column cross-sectional size is generally larger than the thickness of the wall led to the corner convex, which affect the use and appearance, so that the use of the frame structure subject to certain restrictions. Shear wall structure can be arranged along the room layout, and it better match with the building plane, so shear wall structure is more appropriate for the house. From the force point of view, the lateral stiffness is large and deformation is small for the shear wall structure, so the shear wall structure is a system of strong overall resistance especially for high-rise buildings. The weight and lateral stiffness of the shear wall structure are large and vibration cycle is short lead to a larger earthquake load and the increase in the cost of basic engineering, and wall insulation performance of the shear wall structure is also poor. The short-leg shear wall structure can be combined with the building plane and use the location of the partition wall to arrange the vertical components, and the basic function of the building does not contradict. At the same time, the number of walls can be more or less, and limbs can be long and short. The short-leg shear wall structure layout is flexible, and the short-leg shear wall structure have more options available, so the short-leg shear wall structure can more easy to handle the support of the floor. Because of the reduction of the shear wall and replaced by light masonry, the total weight of the house is reduced and the construction speed is accelerated, but there are still shortcoming of poor insulation performance and high cost, especially in the earthquake area has been subject to certain restrictions.

Based on the research and application of these new structural systems and new wall materials, the experts and scholars of building structures in China have pointed out the measures of reduce the building’s weight to improve the defense ability of the earthquake and enhance the energy saving effect and simplify the construction method. In this context, Xi’an University of Architecture and Technology, the General Logistics Department of the Ministry of Infrastructure and other units put forward high-level Multi-ribbed wall frame structure as the new structure. This kind of structural system has the advantages of light weight, large initial stiffness, good seismic performance, good energy saving effect, high construction speed, strong adaptability of structure, high environmental and social benefits, and it is an ideal new structure system. Its development and application conform to the needs of China’s wall material reform, and the high-level Multi-ribbed wall frame structure close connection with China’s national conditions, so the development of the high-level Multi-ribbed wall frame structure is prospects.

Study of Multi-ribbed wall with lightweight frame structure began in 1990, the topic was hosted and finished by Construction engineering institute of new technology of Xi’an University of Architecture and Technology. After 20 years of hard research, The research carried out a large number of detailed and fruitful work in the theory research and applied research, and they obtained a larger breakthrough so that the results of systematic, theoretical and practical [1, 2, 3, 4].

Basic bearing component of Multi-ribbed composite wall of Multi-ribbed wall with lightweight frame structure system is composed of the reinforced concrete rib beam, the reinforced concrete rib column and the lightweight block [5, 6, 7, 8, 9], in terms of structure, compared with the filler wall framework, between frame and filler block are the interaction and coordination deformation in the elastic stage under horizontal load. In elastic-plastic phase, frame and filler block keep close contact on a diagonal direction, but frame and filler block have the break-off phenomenon on the other a diagonal direction. Therefore, Multi-ribbed composite wall simplified as rigid frame-oblique compression bar model has certain feasibility in theory. Built the Multi-ribbed composite wall entity model and the frame-oblique compression bar model to monotonic load calculation under the condition of the same material and size, and analyze stress and strain of Multi-ribbed composite wall entity model and rigid frame-oblique compression bar model through finite element. In the end, comparison and analysis the two models of stress and strain to verify the feasibility of Multi-ribbed composite wall-frame oblique compression bar model.

2. The modeling process of Multi-ribbed composite wall

The mechanical characteristics of the Multi-ribbed composite wall is summarized as follows: the Multi-ribbed composite wall is made of composite material, that is, reinforced concrete ribs, reinforced concrete columns and light-filling blocks. Constraint and anti-restraint effect of the ribs-columns and the filling blocks to the Multi-ribbed composite wall turn to an overall bearing system, and the Multi-ribbed composite wall work together so that common force.

The Multi-ribbed composite wall is composed of two parts: the reinforced concrete frame and the filling block. In terms of structure, the Multi-ribbed composite wall is similar to the frame structure of the filling wall. In the elastic stage, the frame and the filling block is Interaction and coordination deformation under the horizontal load [10, 11]. In the elastic-plastic stage, the frame and the filling block maintain close contact in a diagonal direction, and the frame and the filling block appear the mutual disengagement phenomenon in another diagonal direction [12, 13]. In fact, the filling block can be regarded as the equivalent oblique compression bar; therefore, the Multi-ribbed composite wall can be simplified as a rigid frame compression bar model to analysis and calculation.

Multi-ribbed composite wall is a new type of composite wall, and it choose a reasonable calculation model to simulate is the first. Multi-ribbed composite wall is more complex, and it consists of reinforced concrete frame and filled block, so using a simplified calculation model to solve is feasible.

2.1 The entity model and its material properties

Multi-ribbed composite wall is composed of two parts: frame unit and block unit, and the physical model is shown in Fig. 1.

Where the thickness of the filled block is 100 mm, the ratio of height to thickness is 4, $b$ is 50 mm, $h$ is 40 mm, $B\times H$ is 400 mm $\times$ 400 mm, and the load is selected monotonically loaded. The materials mechanical properties of the frame and filled block are shown in Table 1.

Table 1
Mechanical properties of concrete and building block

Material	Performance
	Compressive strength	Tensile strength	Bulk density	Elasticity modulus
	(MPa)	(MPa)	(kN/m ${}^{3}$ )	(MPa)
Concrete	30	1.43	24	3.0 $\times$ 10 ${}^{4}$
Aerated concrete	7.5	0.65	7	3.0 $\times$ 10 ${}^{3}$

Figure 1.

The entity model.

2.2 The rigid frame-oblique compression bar model

The study of the structural wall system has a long history. In 1949, the Massachusetts Institute of Technology, Stanford University and other research units Conducted a series of experiments about Brick masonry or reinforced concrete frame (with concrete filled block), Until 1990, Zamic put forward A kind of ideal model of the equivalent oblique compression bar [6, 8]. Many scholars at home and abroad through a large number of experimental data and theoretical research to determine the width of the equivalent bar, Smith [7, 9] and others put forward the method, and this method is recognized as a systematic and accurate method among them. Based on researching, the contract stress between the frame and the filling block was supposed, the entity model of Multi-ribbed wall was established by setting contact elements with the materia-nonlinearity and contact non-linearity were considered. The model of rigid frame with diagonal strut for the simplified model of Multi-ribbed wall was solved by the structure mechanics, and the model of finite element was established. The width of the equivalent bar is calculated as follows:

$\displaystyle A_{C}=4\times({400\times 150})=0.24\text{ m}^{2}$ $\displaystyle\eta=\frac{N}{f_{c}A_{c}}=\frac{1\text{ kN}}{7.5\text{ MPa}\times 0% .24\text{ m}^{2}}<0.3$

$N$ take unit force for 1 kN, $\eta<$ 0.3, so $\eta$ take 0.3, and $2\eta+0.4=1$

$\displaystyle Ae=\frac{EC}{Ep}\times AC+Aq=\frac{3\times 10^{4}}{2\times 10^{3% }}\times 0.24+0.4\times 0.4=3.76\text{ m}^{2}$ $\displaystyle b_{2}=\frac{A_{e}}{H}=\frac{3.76}{0.4}=9.4\text{ m}$ $\displaystyle\frac{H}{B}=\frac{400\text{ mm}}{400\text{ mm}}=1$ $\displaystyle K=\frac{0.3E_{p}b_{2}}{\left(\frac{H}{B}\right)^{3}+3\frac{H}{B}% }(2\eta+0.4)=\frac{0.3\times 2\times 10^{3}\times 9.4\times 10^{3}}{1+3}=1410% \times 10^{3}\text{ N/mm}$ $\displaystyle A=\frac{Kd}{Ep\delta\cos^{2}\theta}=\frac{1410\times 10^{3}% \times 400\sqrt{2}}{2\times 10^{3}\times 1000\times\frac{1}{2}}=797.496\text{ % mm}^{2}$ $\displaystyle d=\sqrt{\frac{4A}{\pi}}=\sqrt{\frac{4\times 797.496}{3.14}}=31.8% 7\text{ mm}$

The width of the equivalent bar for $d=$ 32 mm, then the equivalent rigid frame-oblique compression bar model was shown in Fig. 2.

Figure 2.

The equivalent rigid frame-oblique compression bar model.

3. The calculation results and discussion

In the case of the same material, the horizontal load of 20 kN and vertical loading of 15 kN are applied to the entity model and simplified model. The stress and strain of Multi-ribbed wall with entity model and rigid frame with diagonal strut model were analyzed and compared by the finite element to check the feasibility of rigid frame with diagonal strut for Multi-ribbed wall, and the collaborative work mechanism of Multi-ribbed wall was further studied.

Figure 3.

The loading model.

3.1 The entity model calculation result analysis

The horizontal load is 20 kN and the vertical load is 15 kN common load on the entity model. The mapping element division method is used to divide the grid (the grid size is 40 mm $\times$ 40 mm) so that there are nodes with the same coordinate between the reinforcement and concrete and between the concrete and the block. Then, the nodes with the same coordinate are merged in batches to make the joint point coupling and form the overall calculation model, and the loading model is shown in Fig. 3.

After applying the constraint, the entity model under horizontal load and vertical load was calculated by ANSYS, and the relevant calculation results are obtained.

Figure 4.

The first main stress of entity model (Pa).

Figure 5.

The first main strain of entity model (m).

Figure 4 shows first principal stress nephogram of the entity model under the horizontal load of 20 kN and vertical load of 15 kN. We can find that the first stress peak appears in bottom left corner of the lower left corner of the lower right corner frame through the first principal stress nephogram, and its position is the most dangerous point under the horizontal and vertical load.

$\displaystyle\sigma_{r1}=\sigma_{1}=0.21\times 10^{8}\text{ Pa}=21\text{ MPa}<% [\sigma]=28\text{ MPa}$

The first strength theory-the maximum tensile stress theory explains the brittle fracture, the maximum tensile stress of the Multi-ribbed composite wall model $\sigma_{1}=$ 21 MPa is less than the allowable stress $[\sigma]=$ 28 MPa, and it is consistent with the experimental results.

Figure 5 shows the first strain nephogram of the entity model under the horizontal load of 20 kN and vertical load of 15 kN. Apply the second strength theory-the maximum tensile strain theory to verify the calculation, and calculation results conform to the second strength theory.

$\displaystyle\sigma_{r2}=\sigma_{1}-\nu({\sigma_{2}+\sigma_{3}})=\varepsilon_{% 1}\cdot E_{c}=0.651\times 10^{-3}\times 3.0\times 10^{4}=19.53\text{ MPa}<[% \sigma]=28\text{ MPa}$

3.2 Analysis on calculation results of rigid frame-oblique bar model

In the same constraint, the horizontal load and vertical load are applied to the rigid frame-oblique compression bar model, and the results are shown as follows.

Figure 6.

The first main stress of rigid frame-oblique compression bar model (Pa).

Figure 6 shows the first principal stress nephogram of the simplified model under the horizontal load of 20 kN and vertical load of 15 kN. We can see the first principal stress peak is the most dangerous point under horizontal and vertical loads by the first principal stress nephogram,and calculation results conform to the first strength theory.

$\displaystyle\sigma^{\prime}_{r1}=\sigma_{1}=0.158\times 10^{8}\text{ Pa}=15.8% \text{ MPa}<[\sigma]=28\text{ MPa}$

Figure 7.

The third main stress of rigid frame-oblique compression bar model (m).

Figure 7 shows the first strain nephogram of the simplified model under the action of horizontal load of 20 kN and vertical load of 15 kN. Apply the second strength theory – the maximum tensile strain theory to verify the calculation, and calculation results conform to the second strength theory.

$\displaystyle\sigma^{\prime}_{r2}=\sigma_{1}-\nu({\sigma_{2}+\sigma_{3}})=% \varepsilon_{1}\cdot E_{c}=0.528\times 10^{-3}\times 3.0\times 10^{4}=15.84% \text{ MPa}<[\sigma]=28\text{ MPa}$

3.3 Feasibility analysis of rigid frame-oblique compression bar model

Figures 4 and 6 respectively show the first principal stress nephogram of the Multi-ribbed composite wall entity model model and the rigid frame-oblique compression bar model, and the comparison results are shown as follows.

$\displaystyle\sigma_{1}=0.21\times 10^{8}=21\text{ MPa}>\sigma^{\prime}_{1}=0.% 158\times 10^{8}=15.8\text{ MPa}$

The calculation results of the rigid frame-oblique compression bar model are more secure than the Multi-ribbed composite wall entity model, and they meet the first strength requirement. The calculation results show that the strength security reserves of the rigid frame-oblique compression bar model is too large, and the diameter of oblique compression bar can be properly put.

Figures 5 and 7 respectively show the first principal strain nephogram of the Multi-ribbed composite wall entity model model and rigid frame-oblique compression bar model, and the comparison results are shown as follows.

$\displaystyle\varepsilon_{1e}=0.651\times 10^{-3}>\varepsilon_{1s}=0.528\times 1% 0^{-3}$

The calculation results of the rigid frame-oblique compression bar model are more secure than the Multi-ribbed composite wall entity model model, and they meet the second strength requirement. The strain nephogram show that the deformation of the filled block and setting of the rigid frame-oblique compression bar just coincide, which proves that using the rigid frame-oblique compression bar model to simplify the Multi-ribbed composite wall entity model model is feasible.

4. Conclusion

In the case of the same material and the same specimen size, the corresponding stress and strain nephogram of the Multi-ribbed composite wall entity model and rigid frame-oblique compression bar model are analyzed under the horizontal load of 20 kN and the vertical load of 15 kN. The stress nephogram show that the stress changes of the Multi-ribbed composite wall mainly focus on the four corners of frame, and the force of the filled block to frame is mainly oblique support force. The strain nephogram show that the deformation of filled block about Multi-ribbed composite wall mainly showing oblique rod state, and then verify the filled block can be equivalently simplify to a diagonal bar with a certain diameter, and the diameter of the diagonal bar can be determined by the elastic-plastic equivalent calculation.

Analysis on the stress and strain data through the strength theory find that using the rigid frame-oblique compression bar model to simulate the Multi-ribbed composite wall entity model model is feasible, and it can provide effective theory basis for studying the work mechanism of Multi-ribbed composite wall.

Footnotes

Acknowledgments

This work was financially supported by innovation fund projects of UST Inner Mongolia for subsidization (Grant No. 2011NCL056).

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Calculating the rigid frame diagonal strut for Multi-ribbed composite wall

Abstract

Keywords

1. Introduction

2. The modeling process of Multi-ribbed composite wall

2.1 The entity model and its material properties

Table 1 Mechanical properties of concrete and building block

4. Conclusion

Footnotes

Acknowledgments

References

Table 1
Mechanical properties of concrete and building block