Bracing members design according to Eurocode 3 The goal of this article is to prese nt the e fficiency of automatic automatic calculus calculus (done with Advance Design Design)) instead of manual calculus calculus for ve rifyi rifying ng the bracing members against buckling. Automatic Automatic calculus is done for a multi-s multi-story tory stee l concentrically braced braced f rame building subjected to seismic action according to Romanian Rom anian Seismic Code (P100-1/2006). (P100-1/2006). In this structure the most solicited bracing member is studied. The verification results obtained through automatic calculus calculus are in good agre ement with manual calculus. calculus. Click here to download this article as a pdf
General information about steel concentrically braced frames The mos t comm only used configurations of Steel Concentrically Braced Frames (CBF) are illustrated in Figure 1.
Not e: According to P100-1/2 006 006 (Romanian seismic design code), K bracings, in which t he diagonals diagonals intersection lies on a column (see case a ), are not allowed. Figure 1: Vertical bracing Steel Concentrically Concentrically Braced Frames Frames are strong, stiff and ductile, and are therefore ideal for seis mic framing systems. The quality of the seism ic response of Concentrically Braced Frames is determined by the performance of the brace. To achieve the best performance from a CBF, the brace must fail before any other component of the frame does. This is important because although the frame may sustain s ignificant damage during an earthquake, it is expected to to remain s table and the building mus t be capable of resis ting gravity gravity loads and of withstanding aftershocks without collapse.
Note : Slender braces ( a ) are more susceptib le to buck ling than stocky on es and their failure can dam age non-structural ele ments ( b ). On the other hand, strong b races Note: can increase the risk of brittle failure of their connections ( c c ). Figure 2: Failure of concentric bracing members [7],[8] Cyclic testing of conventional braced frames, done by Nathan Canney at Seattle University, showed that these braces buckle in compression and yield in tension. He showed the following inelas tic behavior behavior of bracing mem ber: Plastic hinges occur after the the brace has buckled and the s tiff tiffness ness and resis tance of the frame frame decreases , illustrated in Figure Figure 3; In Zone 0-A, the frame retains its elasticity, but the brace buckles at A, causing a plastic hinge to form in Zone A-B;
Load reversal in Zones B-C, C-D and D-E cause the brace to become uns table, decreasing the effectiveness of the frame. This uns table behavior is evident in the uns ymm etrical response s een in Figure 3a. For this reas on, Concentrically Braced Frames (CBFs), with braces in opposing pairs , are used given the s table inelastic performance seen in Figure 3c.
Figure 3: Behavior of Concentrically Braced Frames [1] The global design objective for energy dissipation in the case of Concentrically Braced Frames is to form diss ipative zones in the diagonals under tension, and to avoid yielding or buckling of the beams or columns. Diagonals in compress ion are designed to buckle. The expected behavior for global mechanism in the case of a frame with chevron bracing (case “f” from Figure 1) is s hown in Figure 4.
Figure 4: Chevron Brace Buckling In this case, when the compres sion brace buckles, the tension brace force doubles (before buckling has 50% of V in the tension brace and 50% of V in the compress ion brace). The vertical component of the tension brace axial force becomes a point load on the beam, pulling the beam down and poss ibly leading to hinging and buckling of the brace frame column. When chevron bracing is us ed, the beam mus t be designed for an unbalanced load when the compression brace buckles. Often the resulting brace frame beam design ends up weighing more than 300 kilograms per m eter. By comparison, when a two story X brace is us ed, when the compression brace buckles at the first floor, the braces at the second floor prevents the brace frame beam from buckling and designing the beam for an unbalanced loading is not necess ary. Design s implifications and practical considerations often result in the braces s elected for some s tories being far stronger than required, while braces in other stories have capacities very close to design targets. Using m anual calculus (in the third chapter) and automatic calculus (in the fourth chapter), this article aims to verify against buckling the mos t strained bracing mem ber from a m ulti-story building and obtain an optimal cross -section.
Modeling the structure. Identification of the most strained bracing member The goal of this article is to find a fast way of an optimum des ign of bracing mem bers against buckling according toEurocode 3. For this purpose it is proposed to design agains t buckling the most solicited bracing mem ber from a m ulti-story building (8 floors) restrained with 2X bracing system (Figure 5). The structure has 3 meters s tory height and 5 meters span (equals on both directions). All structural elements are European steel profiles (s ee Table 1) of S235 steel grade (design values of material properties are s hown in Figure 6). Modeling was done with Advance Des ign and all bracing members were considered pinned at both ends so as to impose axial loads only.
Figure 5. Building 3D view
Figure 6. Material properties The building is s ubjected to horizontal seism ic action (elastic spectral analysis was applied cons idering elastic response spectrum for Vrancea region - severe seism ic area with the des ign peak ground acceleration ag=0.32 g and control period Tc=1.6s ). According to P100-1/2006 elastic respons e spectrum for horizontal components of the field ground acceleration, S e ( T ) is defined as below: S e ( T ) = ag (relation 3.6 from P100-1/2006 [ 6 ]) where ag is the peak ground acceleration [ m/s 2 ].
Figure 7. Normalized elastic respons e spectrum for TC = 1.6s Normalized elastic response spectrum, β ( T ) for fraction of critical damping ξ = 00.5 and depending to control periods TB, TC, TD is states as follows:
where β0 is the factor of maximum dynamic amplification of ground horizontal acceleration by the structure. The loads applied to the structure include relevant load factors and load combination factors. The definition of load cases and load combinations is made as shown in Figure 8.
After Advance Des ign computes the Finite Element Analysis (FEA) we identify the mos t solicited bracing mem ber (with the biggest work ratio; this is element no. 371 SHS 70x8, S235 steel grade, see Figure 9) and the unfavorable case (for this structure, the combination no. 107 is unfavorable: 1x[1 G]+0.4x[2 Q]-1x[4 EY]).
Figure 8. Defining the load cases and load combinations
Figure 9. Bracing mem ber with the biggest work ratio
Manual calculus a) We identify the cross-s ectional characteristics:
- length of the bracing member: L = 3.91m;
b) Calculate the resistance of cross -section, considering the compress ive design axial force N Ed = 336.3kN, which should satisfy:
- γ M0 - partial factor; recommended value by EN 1993-1-1: γ M0 = 1.0
c) Calculate the buckling resistance of bracing mem ber. According to EN 1993-1-1, a compress ion mem ber should be verified against buckling
as follows:
α - im perfection factor --> α = 0.21 (for hot finished hollow s ections and S235 s teel grade we choose buckling curve a); γ M1 partial factor, recommended value by EN 1993-1-1: γ M1 = 1.0;
- Lcr = buckling length; we modeled the bracing not restrained in rotation, so: Lcr = 1.0 · L = 3.91 m;
a) We identify the cross-s ectional characteristics:
length of the bracing member: L = 3.91m;
γ M0 partial factor; recommended value by EN 1993-1-1: γ M0 = 1.0;
α - is imperfection factor -> =0.21 (for hot finished hollow s ections and S235 s teel grade we choose buckling curve a); γ M1 partial factor; recommended value by EN 1993-1-1: γ M1 = 1.0;
We observe that N Ed = 336.3 kN < N cr = 357.2 kN -> the proposed cross-s ection meets the requirement. Note: Eurocode provides a more explicit relationship for memb ers subjected to comb ined bending and axial compression; but the bracing mem bers are not subjected to bending (M y,Ed =0; M z,Ed =0 ), therefore the 2 nd and the 3rd terms of the relationships 6.61 and 6.62, from EN 1993-1-1, are neglected.
Results obtained with Advance Design. Conclusions The next step is to investigate the accuracy of manual m ade verifications; for this we s hall use Steel Design m odule, part of Advance Des ign (AD), which will check if the bracing member has an optimal section according to Eurocode 3; furthermore it will check all structural elements for an optimal section, giving to user the pos sibility to obtain a fast designing and an economical structure. After we have done the Steel Calculation (mod ule of AD for calculating of steel el eme nts), Advance Des ign offers the pos sib ility to see the cros s-s ection characteris tics, the material used for analysis and the s teel grade (Figure 10).
Figure 10. Selected cross section info The strength and buckling verifications are made in the “Cross sections s trength” (Figure 11) and “Elements stability” tabs (Figure 12).
Figure 11. Cross section s trength
Figure 12. Elements stability As we can see, the resu lts obtaine d with Advance Des ign are in agreement with the results obtained with manual calculus. The design load that occurs in the bracing mem ber exceed its capacity (See Figure 13). Advance Design offers suggestions for structural members that provide less resistance. The bracing mem ber with SHS70x8 cross -section has 239.5% work ratio (the same value was obtained with manual calculus) and the program offers SHS90x10.5H cross-section as a suggested solution, with 94.1% work ratio. We can apply this improvement for every cross-section with work ratio bigger than 100% (or any other value of work ratio set by user in calculation assum ptions). Because each project has a different pattern of forces, different member s izes and braced frame elevations we cannot set the s ame optimization method. For this structure, because we have us ed different sections of bracing mem bers for different stories, we can choose an optimization m ethod by section. It is an easy way to obtain an optimal and an econom ical structure.
Advance Des ign aid is ess ential for des ign proces s becau se is les s tim e consum ing (it is prop osi ng the econom ical appropri ate sections for eleme nts with les s resistance) and it is offering the same results as those obtained manual.
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