11th International Symposium on Plasticity and Impact Mechanics, Implast 2016

Numerical based performance of UK industry standard simple and/or semi-rigid steel connections subjected to rapid rotations.

Abstract

The majority of multistory steel framed buildings in the UK are designed such that the connections between the frame elements can be classified as ‘simple’ or ‘semi-rigid’. Current UK design provisions relating to structural integrity and robustness for these types of connections do not currently incorporate dynamic effects such as inertia or strain rate sensitivity. A numerical study has been carried out on a typical UK beam-column simple connection, in which the supported beam connects into the web of the supporting column. The connection has been subjected to a rapid rotation using the finite element software package LS-DYNA. Results and discussion of the numerical study are presented herein; experimental validation of these results is currently being carried out.

© 2016 The Authors. Published by Elsevier Ltd.

Peer-review under responsibility of the organizing committee of Implast 2016.

Keywords: Steel; Connections; Rotations; Impact; Blast; Dynamics

1. Introduction

Highly transient loading conditions, such as blast and impact, are now a very real and necessary design consideration for the structural engineering community. The two topics, in the context of building engineering, have been highly active research areas for a number of years and steel-to-steel connections have been a key focus for many academics and engineers in the field of resilience in the built environment. In the UK, it is common practice for the connections between primary structural elements in a steel framed building (excluding portal frames) to be designed to resist only shear forces in the normal design situation with their ultimate tensile capacity assessed to satisfy any progressive collapse requirements in the accidental design situation. Such design methods consider only quasi-static loading conditions and neglect the dynamic nature of a collapse, blast or impact scenario. The American based design code UFC 3-340-02: Structures to resist the effects of accidental explosions [1] proposes a limiting rotation of 2° at the supports of a steel beam, or a maximum ductility ratio, μ, of 10 (whichever governs) to ensure safety of personnel or equipment, where the ductility ratio is defined as the ratio of maximum dynamic response to the equivalent elastic response of the beam. This rotational limit, when applied to connections typically used for simple braced-frame construction in the UK (such as those in SCI P358[2]) could likely result in the need to re-design the frame as a continuous frame, adding extra cost to a project not only in design fees but in construction costs also.

Progress has been made to understand the true capabilities of such connections when subjected to transient loading mechanisms. Tyas and Stoddart et al. [3-5] subjected typical UK style simple beam-column connections to rapid rotations in a purpose made test rig, and observed increases in peak resistance when compared to quasi-static resistance. Rahbari et al. [6] utilised the same experimental test rig to study angle cleat connections (a form of connection omitted from SCI P358) and observed rotational capabilities of the order 12-14°. There have also been a number of studies [7-10] that have considered UK style connections under sudden column loss scenarios and found it unsafe to rely on static force based catenary action as a mechanism that will arrest the onset of collapse. More recent studies [11,12] that investigate connection behaviour when subjected to impact loading, seek to characterise connections by their energy dissipation capabilities. This falls in line nicely with a preceding study carried out by Szyniszewski and Krauthammer [13] in which the energy flow of a progressive collapse was studied and it was concluded that the ability of any structure to arrest a collapse hinges on its capacity to dissipate kinetic energy, going on to say that future studies may need to focus on energy dissipation.

2. Simple and/or semi-rigid connections typically used in the UK

Existing studies on the topic tend to look at beam-column connections in which the beam connects to the flange of a column square on, as well as this, the majority of studies assume the same grade of steel (S355) is used in practice for the connecting members as for the plate elements of a connection. In the UK, it is almost always the case that the main structural elements (beams and columns) on a project are comprised of grade S355 steel, while any plate material components (flat bracing & plates within connections) are comprised of S275 steel. Bolts within the superstructure connections are usually fully threaded M20 (8.8) bolts and welds are typically 6 or 8mm fillet welds. This is most likely to ensure a connection is classified as ‘simple’ and does not attract any unwanted fixity. SCI P358 recommends any plate elements of a connection be a maximum of 12mm in thickness, bolts be M20 in size and welds be a maximum of 8mm fillet welds. Standard bolt pitch (vertical spacing) is 70mm and the gauge (cross centres) is set at 90mm for connections where the connecting beam depth is up to 533mm, and set at 140mm beyond that, assuming M20 bolts are used. If a connection is specified beyond these recommendations, then it is more likely to be classified as ‘semi-rigid’ than ‘simple’ in accordance with EN1993-1-8 [14]. The additional rotational stiffness properties that semi-rigid connections possess are seldom utilised in the design of structures in the UK. A survey conducted on the UK steel construction industry [15] indicated the most preferred form of simple and/or semi rigid connections to be full depth end plates followed by partial depth end plates and then fin plates. The connection studied here-in examines the numerical based performance of a partial depth end plate connecting into the web of a supporting column.

3. Numerical Model

A numerical model has been built of a partial depth end plate connection between a 305x127x37 UB and a 203x203x46 UC using the LS-DYNA finite element code. The end plate was 150mm wide, 220mm deep and 10mm thick, it was welded to the 305x127x37 UB section with a 6mm fillet weld. The plate then connected to the web of the 203x203x46 UC section, along centre lines, with 6No M20 bolts in two lines at 90mm gauge and positioned with 70mm pitch emanating from the centre of the end plate. The grade of steel of the two open sections was treated as S355, the grade of the end plate treated as S275 and the grade of the bolts treated as grade 8.8. It was assumed the weld inherited the same material properties as the end plate. The numerical model resembled a drop hammer test which is to be conducted on the specimen at a later date. An engineering drawing of the drop hammer test is shown in Fig. 1.

Fig. 1. Physical drop hammer test set up for connection under numerical investigation

The numerical model (Fig. 2) was constructed and analysed using a systematic process. Firstly, the mesh was created using Altair HyperMesh, then exported into Oasys PRIMER where the keyword file was built. Once the keyword file was completed, the model was loaded into LS-DYNA and the analysis was performed. Post-processing was done using LS-PrePost. To get an accurate representation of an in-situ connection, the bolts were assigned a clamping force of 75kN each at the very start of the analysis. After this clamping force had been initialised, an axial force equivalent to 75% of the design shear capacity of the connection (in accordance with SCI P358) was put through the column web and kept there throughout the duration of the simulation. The displacement-time history that simulated the drop hammer commenced once this axial force had also initialised. A dynamic simulation in which the model was taken to failure in under 10ms was carried out as well as a quasi-static simulation.

Displacement-time history applied to node set here Top of 305x127x37 UB fully restrained (a) Whole model (b) Close up of connection zone (c) Isolated bolt, bolt head and nut (d) Close up of weld

Fig. 2. Numerical model of drop hammer test

The input displacement-time history used for the dynamic analysis was as Fig. 3a. When dealing with blast or impact problems, it is perhaps more useful to visualise the applied loading as a force-time history plot. To obtain this, the 203x203x46 UC section was idealised as a rigid bar and the partial depth end plate treated as a true hinge about which the bar could freely rotate (as would be the assumption in design). The change in rotational kinetic energy was then calculated using the mass moment of inertia of the 203x203x46 UC and the average rotational velocity at each time step. By applying the work-energy principle, the value of torque at the hinge could then be calculated and thus an approximate impact force back calculated as the level arm is known. This approximated force-time history plot is shown in Fig. 3b.

(a) Input displacement-time history as used in analysis (b) Approximated equivalent force-time history

Fig. 3. Input loading data for numerical simulation

It should be noted that Fig. 3b is only an approximated input force-time history as an assumption has been made that the 203x203x46 UC will act as a rigid bar, in reality it will deflect with curvature because the connection to the 305x127x37 UB offers some resistance to deformation. Basic analytical modelling of the global system is not possible unless the amount of fixity the connection offers is known and the system is a mechanism if the connection is modelled as a pin. It is not the intention of this paper to apply any component models to the connection as this is scope for future works of this study once a robust numerical model is in place.

The geometry of the 305x127x37UB and 203x203x46 UC was created in line with the dimensions found in the Tata steel sections interactive blue book [16]. The web of the UB section was given a mesh seeding of 2 across its thickness which gave 3.6mm elements, and a mesh seeding of 1 across its flange thickness, which gave an element thickness of 10.7mm. Whilst it is generally not considered good practice to mesh a thickness with only 1 element, it was deemed acceptable here as the majority of the force was anticipated to act away from the flanges of the UB section. Longitudinally, the UB was assigned a mesh seeding of 3 for the first 6mm, giving an element length of 2mm, and then a seeding of 20 for the remaining 194mm giving an element length of 9.7mm. This staging of longitudinal mesh density was done so that the nodes of the elements in the first 6mm could be merged with the nodes of the elements that form the weld.

The web of the UC section was assigned a mesh seeding of 4 across its thickness, giving 1.825mm elements and a seeding of 2 was applied across the thickness of its flanges giving 5.5mm thick elements. Longitudinally, the UC section was first meshed with a seeding of 10 for the first 53.44mm from the connection end and then the remainder of the UC length was given a seeding of 120 which gave an element length of 11.67mm. The UC mesh density was higher for the first part of its length from the connection end because contact was anticipated between the web of the UC and the corner flange of the UB.

The end plate was meshed firstly by creating an evenly spaced regular 2D grid on plan that accounted for the spacing of the bolts, the location of the weld, length and width of the plate, web of the UB section and anticipated location of plastic hinge formation. Once this 2D grid of elements was created, it was projected through the thickness of the end plate (10mm) with an element seeding of 5. Plastic hinges were anticipated to form either side of the welds so mesh density was increased in these regions.

Only the throat thickness of the weld was modelled, the geometry of which was in accordance with SCI P358 for a 6mm fillet weld, hence the triangular shape in Fig. 2d. The horizontal and vertical edges of the weld were both assigned a mesh seeding of 3 giving an element length of 2mm. Longitudinally the mesh seeding was assigned such that the nodes on the surface of the end plate and the nodes on the weld coincided and could be merged. The geometry of the bolt shanks, bolt heads and bolt nuts were obtained from SCI P358 and meshed with solid elements.

In total the model comprised a purely Lagrangian mesh of 40,210 fully integrated solid elements and 55,158 nodes. The only boundary condition set on the model was to the nodes at the top of the 305x127x37 UB which were fully restrained (Fig. 1a). A surface to surface, penalty method based contact algorithm was employed with a friction coefficient of 0.2 for both static and dynamic friction at all contact interfaces.

4. Material constitutive relations

To capture material behaviour under a blast or impact scenario, a constitutive relation that captures the effects of strain hardening, strain rate sensitivity, temperature softening, varying stress states and history of loading is required along with accumulation of damage and failure [17,18]. A material model that fits these criteria and is commonly used for such scenarios is the Modified Johnson-Cook (MJC) constitutive relation [19] in which the equivalent flow stress is computed as:

(1)

where A is the yield strength, B and n are parameters that capture the effects of strain hardening, C is the strain rate constant and m is the thermal softening parameter. is the equivalent plastic strain, is the equivalent plastic strain rate, and is the reference strain rate at which parameter A was determined. is the absolute temperature, is the room temperature, and is the melting temperature of the material. The duration of the impact loading mechanism was short enough that heat conductivity could be neglected and only adiabatic heating accounted for. The temperature increment for this was calculated as:

(2)

where is the Taylor-Quinney coefficient, is the material density, and is the specific heat capacity.

Failure was captured using the Cockcroft-Latham (CL) fracture criterion [20] which states that failure occurs when the plastic work per unit volume exceeds a critical value . This is expressed mathematically as:

(3)

where is the maximum principal stress, when and when . The parameters A, B, C, n, m and Wcr can all be derived by uniaxial tensile testing. For S355 steel and Gr8.8 bolts, Grimsmo et al. [11] derived the parameters for a material model that was a slight variation of the MJC model utilising Voce hardening parameters. The parameters A, B and n for the present study were obtained by curve fitting the left hand bracket of Eq. 1 to the stress-strain plot for the two respective materials when using the model employed Grimsmo et al. The same value of strain rate parameter C was used as in the study by Grimsmo et al. as was the value of Wcr. For the S275 steel, a tensile testing programme is currently in progress and working values of A, B, n and Wcr have been used, engineering judgement has been used for parameter C.

All of the materials were assigned the same temperature related parameters, these were adopted from Borvik et al.[21] and are typical for steels. These were as follows: , K, K, and J/kg K. Table 1 presents the values of the material parameters used for each grade of steel in the model.

Table 1. MJC and CL material parameters used in numerical model.

A (MPa)	B (MPa)	n	C	(1/s)	(MPa)
S275	310.29	650	0.6	0.05	0.0004	467.9
S355	413.7	523	0.46	0.016	0.001	786
Gr 8.8	874	400	0.44	0.011	0.001	1311

5. Observations

Tearing of the end plate was the failure mode for both the quasi-static and dynamic simulations. This occurred in the regions immediately adjacent to the weld. A time-history of the dynamic simulation is depicted in Fig. 4 commencing at the first time step of the drop hammer impact. The view is looking toward the connection from the drop hammer. Immediately after impact (Fig. 4b) the end plate begins to bend with the web of the UC section convexly around the web of the UB section. The displacement under the drop hammer then causes a pull-down force at the front of the plate via the bolts, causing the plate to cease bending convexly, straighten out (Fig. 4c) and then begin to bend concavely (Fig. 4d). At the same time as this, though not well depicted, the web of the UC section continues to bend convexly at the rear of the connection. These two modes of bending continue throughout the remainder of the simulation. Separation occurs between column web and plate at the front of the connection (Fig. 4e-g). The deformation of the end plate before tearing is depicted in Fig. 4h showing the convex bending at the rear of the plate and concave bending at the front of the plate. This difference in modes of bending creates a point of contraflexure longitudinally in the plate and is likely a result of the web being a higher grade steel (S355) to the plate (S275), at the same time as being thinner and therefore possessing more flexibility capabilities than the plate. Current design provisions (SCI P358) assume that the web will fail before the plate when providing provisions for progressive collapse in the design of beam-column web connections.

Each bolt deformed with the direction of plate bending local to it and none of the bolts remained upright. This allowed the direct tensile stresses in them to be somewhat relieved and prevented them from failing in direct tension.

The web of the UC section impacted the corners of the UB at the rear of the connection (Fig. 4i). The effect of this contact appeared to have only little bearing on the overall connection performance. The corners of the UB were crushed by the initial stage of contact, and then shortly after equilibrium is reached locally the connection fails. By contrast, this contact would put the whole end plate in a beam-column flange connection into tension as the flange would remain rigid throughout the analysis, such behaviour was observed by Stoddart et al. [22].

(a) t=0s (b) t=0.0015s (c) t=0.003s (d) t=0.005s (e) t=0.007s (f) t=0.0104s (g) t=0.0125s (h) End plate only after failure. (i) UC web impacting corners of UB at rear of connection.

Fig. 4. Dynamic simulation damage evolution

6. Results

The moment-rotation curve for both the quasi static and dynamic simulations are depicted in Fig. 5.

Fig. 5. Moment-rotation curves for connection

An increase in moment capacity from the dynamic simulation can be observed coupled with a reduction in ductility. This is likely to be due to strain rate sensitivity. The moment at the very start of the dynamic simulation is negative with a small amount of negative rotation due to the convex bending of the plate discussed in section 5. The average strain rate to failure for the first element to be eroded was 49.8/s which is within the range proposed by Barata et al.[23] for impact loading. The flexible nature of the column web causes the centre of rotation to vary throughout both simulations and as a result very non-linear responses are encountered. In both simulations yielding of the end plate occurs before 1° of rotation at a moment of around 33kNm statically and 45kNm dynamically. The ultimate moment capacity for the connection was 77kNm statically and 89kNm dynamically at rotations of 6.33° and 4.88° respectively. This provides a Dynamic Increase Factor (DIF) of 1.16.

7. Validation

Experimental validation is required for this numerical model coupled with the implementation of an appropriate component model. A test programme at the University of Liverpool Blast and Impact Research Centre is currently being planned to facilitate this. Some qualitative validation is provided in Fig. 6. The physical test specimen photographed is of a partial depth end plate connection that formed a connection to a column flange. No convex plate bending is apparent in the experimental photo. Stoddard et al. [4] observed ultimate moment capacities of 80kNm and 100kNm for a similar connection that connected to the column flange, giving a DIF of 1.25.

(a) Photo of beam-col flange connection subjected to rapid rotation testing. (b) Present numerical simulation just before failure, connection was beam-column web

Fig. 6. Qualitative validation of model

8. Conclusion

It was the intention of this paper to present the findings of a numerical study on a simple connection that is typical of those used in the UK when subjected to a rapid rotation. The connection investigated was a partial depth end plate connection between a supported beam and a supporting column web. The following conclusions can be inferred from this study:

The failure mode of beam-column web connections when using a 10mm thick partial depth end plate to connect a supported beam and supporting column is likely to be tearing of the end plate, in the zone adjacent to the weld, if S275 grade steel is used for the plate and S355 grade steel used for the column. Current UK design guidance presumes column web failure as the governing failure mode when providing provisions for progressive collapse prevention.

Both concave and convex bending will be encountered by the end plate when a partial depth end plate connection is subjected to a rapid rotation that connects into the web of a supporting column. A point of contraflexure is created longitudinally in the plate as a result. This complex bending deformation causes complex non-linear behaviour within both the elastic and plastic regions of the moment-rotation response curves.

Moment capacity is increased when a partial depth end plate connection is loaded dynamically while ductility is reduced. A DIF of 1.16 was observed, although the DIF for a similar connection detail that connected to the flange of a supporting column was 1.25. This reduction in DIF is believed to be due to the flexibility of the column web.

Contact forces between the column web and the bottom flange of the supported beam do not appear to have an effect on connection performance.

Further validation is required for this study.

Acknowledgements

This research is funded by the Engineering and Physical Sciences Research Council (EPSRC ref EP/L505018/1) and the Institution of Structural Engineers Research Award for 2015.

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