Applied Research on Wide and Flat Beams

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Application Research on Wide and Flat Beams Abstract: Due to limitations in building floor heights, the design of wide and flat beams has been widely adopted in recent times to improve indoor space utilization. In the design of the covered playground at Tianjian Century Garden Primary School some time ago, the author used wide and flat beams, which gave him further insight into the application of such beams. Keywords: Wide flat beam Project overview: The indoor sports court of Tianjian Century Garden Primary School is a three-story frame structure; it features large open spaces in certain areas, with reinforced concrete independent column foundations being used for the base. Due to the requirement for a lightweight and simple architectural facade, the height of the beams in the partial side spans of the third floor (the top floor) is limited to 500. The top floor adopts a closely spaced ribbed beam structural system. The beams on the 11-A and 11-5 axis sides are wide and flat beams, with cross-sectional dimensions of 1000x500 and 600x500 respectively; upturned beams are used, and the plan layout is shown in Figure 1 below. 　　Design of wide and flat beams: Regarding the design of wide and flat beams, the 2001 seismic code only specifies requirements for their cross-sections, without providing detailed guidelines. Referring to domestic and international abstracts and papers, foreign scholars believe that the force balance in the node area is crucial; if some of the rebar in the wide beam passes outside the column, there will be no vertical forces at the upper and lower ends of the diagonal compression members to provide balance, and the portion of the beam outside the column may be sheared apart. Based on this, they proposed two solutions: 1. Place all the rebar in the upper part of the beam within the column width range ； 2. Install vertical reinforcement to bear the vertical component of the thrust generated by the compression bar. 　　Referencing domestic literature, the first method is only applicable when the beam is slightly wider than the column; otherwise, the rebar inside the column becomes so dense that construction becomes impossible. It is also unreasonable to use multiple rows of rebar at the expense of the beam’s effective height. However, we require that around 70% of the rebar pass through the column. Regarding the second method, there are many specialized discussions in China. Experiments have shown that under static and low-cycle repeated loading, the failure zone of wide flat beams is primarily in the core area outside the joints. Installing stirrups in the outer core area helps to protect the inner core and transfer plastic hinges; moreover, it is necessary to include vertical rebar running through the columns to enhance the strength of the outer core area. In summary, in node design, the torsional resistance of the core area outside the node is the key aspect of wide and flat beams. 　　Configuration of horizontal shear stirrups in the core area of frame joints: In addition to being installed in the columns within the inner core area in accordance with the requirements of current codes for concrete structure design, horizontal shear stirrups should also be placed around the outer core area. The required specifications are as follows: For seismic resistance grade 1, ≥φ12@100; for seismic resistance grades 2 and 3, ≥φ10@100; for non-seismic structures, ≥φ10@200. For two-way wide and flat beam joints, these stirrups can be formed by using the vertical stirrups of the wide and flat beams that run in both directions. A one-way wide and flat beam joint can be formed by using the web reinforcement of the wide and flat beam running in both directions, along with additional horizontal tie reinforcements in the opposite direction. 　　Configuration of torsion-resistant longitudinal reinforcement in the outer core area of frame nodes: When the heights of bidirectional wide and flat beams are equal, it is advisable to increase the longitudinal reinforcement of the frame beams as required by the calculations ； When the heights of the two-way wide flat beams are different, upward-opening stirrups can be added at the bottom of the core area in the direction of the shorter wide flat beam to form bottom torsion-resistant longitudinal bars ； In the case of a one-way wide and flat beam, it can be formed by providing additional closed stirrups in the node core area (which functionally is equivalent to the stirrups of the wide and flat beam extending into the node core area). 　　When an additional restraining stirrup is used, the construction requirements are as follows: 　　 For seismic resistance grade 1: ≥φ12@100 　　 For seismic resistance grades 2 and 3: ≥φ10@100 　　 For non-seismic grades: ≥φ8@100 　　Regarding the torsional restraining stirrups around the core area outside the frame joints: 　　 These are established by using additional vertical tie bars at the corners of the outer core area, which are welded or lapped to the longitudinal reinforcement of the wide and flat beams in that core area, in accordance with the calculation requirements. 　　The structural requirements for additional vertical tie bars are as follows:
For seismic resistance grade 1: ≥φ12@100
For seismic resistance grades 2 and 3: ≥φ10@100
For non-seismic grades: ≥φ8@100

Regarding the vertical shear reinforcement in the core area outside the frame joints:
Vertical shear tie bars should also be installed within the core area outside the frame joints to serve as shear reinforcement; these tie bars should engage with the longitudinal reinforcement of the wide and flat beams that enter the core area and be tied to it. The structural requirements for these tie bars are as follows:
For seismic resistance grade 1: ≥φ10@100
For seismic resistance grades 2 and 3: ≥φ8@100
For non-seismic grades: ≥φ8@100

During the calculations using the SATWE program for this project, no abnormalities were detected in the results related to wide and flat beams, which indicates that the program does not take this factor into account. Therefore, further verification is necessary. The column width is 500, the beam height is 500, and the beam widths are 1000 and 600 respectively; calculations show that they meet the requirements regarding load capacity and structural integrity. Taking Figure 5 as an example to verify the shear capacity of the frame joints in the 11-3 axis system: The design value for the horizontal shear force at the frame joints made of wide and flat beams is determined in accordance with the current codes for concrete structure design. According to the results obtained from SATWE, V = 419 KN and N = 466.09 KN. The design value for the horizontal shear capacity of these frame joints is given by: VJ = ρRE, with the condition that VJ ≤ (0.3ηJfcbJhJ) / ρRE. Here, ρRE is the adjustment factor for shear capacity considering seismic effects; ηJ is the coefficient reflecting the restraining effect of the wide and flat beams on the joints; N is the design value for the axial compressive force on the columns at the joints, also taking into account seismic effects. When N > 0.5 fcbchc, N is taken as 0.5 fcbchc. bJ represents the effective width of the horizontal shear section within the core area of the frame joint, while hJ is the height of this horizontal shear section, which is generally equal to the width of the core area outside the joint. a’s is the distance from the centroid of the compressive steel bars in the wide and flat beam to the edge of the compressed zone. fyv is the tensile design strength of the horizontal stirrups within the frame joint. Asv is the sum of the cross-sectional areas of all horizontal stirrups in the same horizontal section that act in the same direction as the horizontal shear force. S is the spacing between horizontal stirrups along the vertical direction within the frame joint area. bb is the width of the cross-section of the wide and flat beam, hb is its height, hb0 is also its height, and b0 is the effective width of the horizontal shear section in the core area outside the frame joint. Thus, VJ ≤ (0.3ηJfcbJhJ) / ρRE = (0.3 × 1.83 × 12.5 × 750 × 500) / 0.85 = 3027.6 KN, which meets the design requirements. 　　The flat-width beams in this project are frame edge beams; in addition to the torsional reinforcement required to ensure proper torsional resistance, it is also necessary to take into account the additional shear forces transmitted from the flat beams in another direction to the frame edge beams. Reinforcement should be increased appropriately in these areas. Figures 2 through 5 show several typical joints in this project. 　　Several issues to consider in the design: After conducting numerous calculations on the cracks in wide and flat beams, it was found that for beams controlled by strength requirements, if the reinforcement ratio is high, the crack width will not meet the specified limits, necessitating an increase in the amount of reinforcement. Based on experience, when the reinforcement ratio reaches around 2%, attention should be paid to crack issues. 　　 When checking the deflection of wide and flat beams, stiffness plays a decisive role when the support conditions and span are fixed. The formula for short-term stiffness is as follows: Bs = EsAsH02/. The effect of the flange (γ’f) is often overlooked by us, but in reality it has a significant impact. Furthermore, wide and flat beams should not have double rows of reinforcement. An increase or decrease in H0 has a significant impact on the results. The code stipulates that: \"The deflection of flexural members shall be calculated using the short-term effect combination of loads, taking into account the long-term stiffness BL influenced by the long-term effect combination of loads.\" ”In the long-term stiffness formula: BL=MSBS/. The larger the proportion of dead load, the smaller BL becomes relatively, and the greater the deflection. Therefore, when the permanent load on the roof deck is relatively large while the live load is small, it is even more necessary to check the deflection of the beams and slabs. 　　When calculating plates supported by wide and flat beams, for elastic analysis, the span values for multi-span continuous plates are determined using the following formulas: For the end spans: L = L0 + a/2 + b/2; L ≤ L0 + h/2 + b/2. For the intermediate spans: L = L0 + b; L ≤ 1.1L0. In fact, these formulas are not appropriate for wide and flat beam structures. Research shows that the behavior of the plate in the area where it overlaps with the wide and flat beam is completely different from that of a pure plate; rather, it acts in conjunction with the beam and coordinates with it. By considering the plastic redistribution of internal forces in the slab, the bending moment required for calculating the mid-span section of a slab that is connected to beams on all four sides can generally be reduced by 20%. In fact, due to the positive bending moment at the mid-span of the continuous slab, cracking occurs in the lower part of the cross-section, while due to the negative bending moment at the supports, cracking occurs in the upper part of the cross-section; this causes the actual axis of the slab to assume an arch shape, with the arch-shaped supports located near the edges of the beam. Based on the above theoretical basis, we take the calculated span of the plate to be L = L0 + h (where h is the plate thickness). 　　 When calculating the reinforcement for slabs, general construction manuals specify that the length of the negative reinforcement in two-way slabs should be L1/4 (measured from the axis). In typical beam-slab systems, the negative bending moment can basically be fully accommodated by this reinforcement. However, for wide and flat beams, using such values is clearly unreasonable. We believe the reasonable value is L0/4 + b/2 (where L0 is the net span of the slab). 　　References and Literature 　　1. Code for Design of Concrete Structures (GBJ10-89) 　　2. Fu Xueyi: Design Rules for Wide and Flat Beams (1998) 　　3. Lian Xianrong et al.: Experience in the Use of Wide and Flat Beams – Large-Span Slabs (Case Study: Shekou China Merchants Shopping Center) 　　4. A.H. Nelson, G. Windell: Design of Concrete Structures (translated by Guo Zhenhai et al.) 　　5. Zhou Qijing et al.: Manual of Concrete Structure Construction (1994)