## Structural stressing

As part of a major expansion drive of a large multinational organisation, additional office space is required. The location of the building is the financial district in the Docklands area to the east of London. The client has requested that the building will reflect the strength of the organisation. As such the quality of the design must be of the highest standard as the building will be an important landmark in the city. Special attention must be paid to the ground floor, with increased storey height (‘storey 0’).

Due to the volume of office space required and the limited space available the client has stipulated that the building must have a minimum height of 230 metres and not exceed 250 metres with a gross enveloped volume not greater than 0.5106 m3.

IMPLEMENTATION AS MSc PROJECT

To increase variety in the submissions and provide an investigative component to the project, students are required to address additions to the Client’s specification. In particular, one option should be considered in detail which is likely to require a feasibility study. Options include (although not an exhaustive list):

• Upper 30% of height arranged for residential (domestic or hotel) occupancy,

• Storeys 2 & 3 arranged as dealing floors including clear spaces >300m2,

• Upper 30% of height offset (compare Palaestra project, NSC April 2005 p20),

• Full-width ‘airspace’ development over water (dock) (compare Broadgate 11),

• Provision of hotel ballroom/gymnasia >200m2 suitable for rhythmic group activities,

• Effect on bracing design in a seismic zone,

• Investigate subjective comfort effects of sway and wind effects,

• Investigate robustness issues associated with terrorist activity.

• Fire engineering aspects.

• Design of foundations.

• Design of Composite mega-columns

BASIS FOR DESIGN

Standards

EC3 should be adopted for the basis of the structural steelwork design. Composite construction is also permitted where it is deemed suitable and EC4 should be referred to. It should be pointed out that the design codes will only play a small part in the design process as the structure is not a routine design covered by most codes of practice. Your conceptual design phase, parametric investigations of schemes and justification of how you arrived at your final design is far more important. This will involve significant hand calculation, particularly in the early conceptual phase, and eventually the use of software to fine tune your final design.

Loading

Dead Self weight as found

Superimposed (ceilings, services+raised floor) 0.90 kN/m2

Cladding 0.5 kN/m2

Glazing panels 0.5 kN/m2

(i) Imposed

Office floor areas 5.0 kN/m2

Domestic floors (where applicable) 3.0 kN/m2

Plant levels 7.50 kN/m2

(ii) Wind and snow

EN1991-1-4 with appropriate UK National Annexe using basic wind speed map and snow s0=0.5 kN/m2

Wind data attached in appendix A.

Serviceability requirement: as appropriate for a prestige building.

SUBMISSIONS

The submission should consist of a single report to include calculations and drawings of your proposed scheme using single sided A4 sheets and sufficient drawings to show the design intent.

The submission should include the following:

(a) Report

A maximum of 40 pages of double spaced text with a minimum font size of 11 which must cover:

(i) A description of the structural arrangements;

(ii)A description of how the layout of the building is organised;

(iii)An outline of the design process that led to the development of the final scheme. This should include a feasibility study of two schemes showing preliminary calculations to estimate member sizes and parametric investigations to justify selection. Your two schemes should adopt different lateral load resisting systems such as outriggers, mega bracing, diagrid, framed tube, mega-columns. This is not an exhaustive list and of course as shown in the introduction to tall buildings hybrid lateral load resisting systems can be used adopting more than one type.

(iv)A brief description of the proposed methods of construction should be given. This need not be quantified or described in detail but they must be feasible; the problems that might be encountered during construction should be discussed, together with the steps that might be taken to overcome them;

(vi)A separate section dealing with your chosen special topic.

(b) Calculations

These must include all the detailed calculations to confirm the adequacy of the main structural members proposed. This should include the detailed design of typical connections. Appendices may also be used to help you present the calculations in a logical manner. The appendices must be paginated and cross referencing used to easily locate values in calculations used.

(c) Drawings

One print of each drawing, folded to standard A4 size. The drawings must indicate all relevant dimensions, and must show:

Plans, elevations and cross sections of the proposed structure, at preferred scales of 1:200 for plans and elevations, and 1:100 for cross sections. It should show relevant member forms and sizes, and give general specifications.

Typical details – e.g. connections, cladding and glazing interfaces, etc at a preferred scale of 1:20.

(d) OVERALL PRESENTATION

The overall presentation of the report is a critical aspect of presenting any design calculations to a senior engineer/client. The brief should therefore appear, concisely presented. Calculation-sheet format is desirable, whether or not handwritten or word-processor produced – this means that every page carries a heading identifying the specific subject content of that page, and a means of highlighting the input and output (recommendation) with appropriate page cross-references. Cogent and Concise remain the key characteristics.

Drawings should be provided which clearly communicate the structural intent for the two designs.

Preliminary drawings should be provided for the schemes which has only been taken to concept stage. These should outline the:

• Overall dimensions including:

o floor to floor height

o column grid dimensions

o overall structural depth of the floor.

• Proposed lateral stability system:

o Annotation should describe the structural behaviour of the system.

o Overall dimensions should be given for the most critical structural elements.

Drawings with more detail should be provided for the detailed scheme. These should include:

• Typical floor plan(s), giving sizes for the structural elements and the column grid dimensions.

• Elevation(s), giving floor to floor height.

• Drawings of the lateral stability system:

o Plan(s) of the system giving sizes for the structural elements.

o Elevation(s) of the system giving sizes for the structural elements.

o Drawings should be annotated to describe the structural behaviour of the system.

• Principle structural connections.

• Section to show how the minimum required floor to ceiling height is achieved.

Calculations should be provided which clearly show how the design proposals given on the drawings satisfy the relevant ultimate and serviceability limit states for vertical and lateral loads.

Finally, all pages must be consecutively numbered and prefaced by a comprehensive reader-friendly Table of Contents that enables the reader (your Client) to home-in directly on any selected design decision.

Appendix A

Wind Load for design of a tall building.

Interpretation/ application of EN1991-1-4 and UK NA.

Building approx h=250m high at location in London Docklands (about 10km east of Imperial College campus): vmap=21.4m/s. Level ground, altitude 10m. No specific local shelter (x>6h {EN A5}). Notation b = building face width (m), z = height above ground level.

To evaluate basic wind velocity vb, note cprob and cseason inapplicable, and take cdir=1.0 on assumption that at least one critical load case will come from an unfavourable wind direction (quadrant 210o to 300o). The altitude factor in NA2.5 is a UK concept that fits rather awkwardly, but has minimal impact for such a low site altitude, so evaluate calt,s (eq NA2b) at (say) zs=0.6h=150m and take this as applicable at all levels, vb,0= calt,s vmap (eq NA1)

(i.e. giving a ‘fudged’ value for vb,0 avoiding the complication of calt varying with z).

The wind profile with height comprises mean speed factor cr(z) and intensity of turbulence (rms fluctuation divided by mean) Iv(z) as a function of ‘fetch’, i.e. the terrain roughness and distances. As the terrain is flat, we have no ‘orography factor’ to consider (co=1.0, EN eq4.3).

The EN has a very poor formulation of the way the wind profiles change in response to passing from one terrain category to another, so the NA gives a comprehensive reformulation based on the work of Harris and Deaves (similar to the BS, BS6399pt2, see also ESDU data items). The five EN terrain grades are simplified to three, ‘sea’, ‘country’ and ‘town’, with charts to interpolate as a function of the fetch distance to the site. For the project example, >100km from the coast and > 20km from open country in the quadrant mentioned above, the ‘town’ profile is dominant. The target is evaluation of the peak kinematic pressure q=½ρv2 (‘velocity pressure’ in Eurospeak) (note ½ρ=0.613×10-3t/m3), but here also the NA differs from EN eq4.8,

qp(z) ={1 + 3Iv(z)}2.½ρvm2 = ce(z)qb. (eqns NA3a, 3b)

cr(z), Iv(z) and the derived factor ce(z)={1+3Iv(z)}2cr(z)2 (actually with marginal empirical adjustments) are conveniently presented in chart from, figs NA3 to NA8, e.g. key values

z 50 100 150 200 250 m

cr(z) 1.092 1.263 1.360 1.439 1.521

Iv(z) 0.207 0.180 0.156 0.140 0.129

ce(z) 3.12 3.82 4.01 4.20 4.40

The resulting loads (pressures) acting locally are given by we= qp(z)cpe (subscript ‘e’ indicating ‘external’). The cumulative action of these pressures is then modified by

- factor cs expressing imperfection of correlation of the gust actions over the loaded area, eq6.2
- factor cd allowing for augmentation of load effects by dynamic response to gusts, eq6.3.

The procedure for evaluation of the parameters B, R and kp endorsed by the NA is EN Annex B, eqnsB3 to B8, but for all except the final check, NA2.20 with Table NA3 and figure NA9 gives a much more user-friendly option. Eqns B3 to B8 are essentially the classic Davenport formulation, but some caution may be desirable because the change to a 10-minute averaging time reduces the implicit ‘cycle count’ (‘up-crossing frequency’ times averaging time) to a degree that increases statistical uncertainty, and the scale parameter used in eqnsB7, B8 is perhaps non-conservative. Structural damping should be taken as 0.05 logarithmic decrement (EN Annex F). As this structure is likely to be moderately dynamically sensitive, you should perform the full evaluation once you have an estimate of the natural frequency – this is unlikely to have a severe effect on stresses, but may require consideration of subjective comfort (lateral sway in strong winds).

For evaluation of the loading on a prismatic building, simple ‘strip theory’ in which qp(z) is treated as a continuous function of height z following directly on ce(z) is not permissible. This is because the pressures for a considerable part of the height are substantially influenced by the speed at the top of the building. The required evaluation of qp(z) for the front (upwind) face (zone D, see below) is defined by EN fig 7.4 (clause 7.2.2 (1)), and for the rear (downwind) face (zone E), the value at the top, qp(h) is used for the full height. The respective external pressure coefficients cpe are given in EN table 7.1; cpe,10 values are used for all loaded areas exceeding 1m2 (NA2.25). These pressures cover values for the worst location on the face, and the NA offers a simplified ‘net pressure coefficient’ (Table NA4 – NA2.27) for the overall-average loading that gives significantly lower values (cs allows for imperfect correlation of wind gust action, not for variation from point to point of the mean value). This is presumably to be used in conjunction with qp(z) as defined for the upwind face. At h/d=4 (where d is the alongwind dimension of the prism) the net coefficient from table NA4 is 1.25, compared to the sum for two faces from EN table 7.1 of 1.45. In both cases it is permissible to make a further reduction to account for lack of full correlation between the faces of the gust action, EN 7.2.2 (3) NOTE, although this tapers out at h/d=5. In the case of h/d=4, this factor is 0.96.

The base cases are winds perpendicular to a face, thus generally forces for two orthogonal wind directions. This will generally cover critical ‘shear’ checks on the lateral-resistance system, but it is usual for ‘bending’ checks to prove critical with diagonal-direction winds (consider the column forces in a frame square in plan; the effective section modulus for diagonal-plane bending is only 1/√2 times the value for plane-of-face bending). Remarkably, neither the EN nor the UK NA address this problem, and it is therefore necessary to seek ‘NCCI’. An obvious choice is the British standard on which much of the UK NA was based, BS6399 part 2. This comprises two methods, ‘standard’ and ‘directional’. The ‘standard’ method includes in §2.1.3.6 “Where the combination of the orthogonal loads is critical . . . the maximum stresses caused by wind . . . may be taken as 80% of the sum of the wind stresses resulting from each orthogonal pair . . ”. The ‘directional’ method gives values of design face pressures at 15o increments of direction (§3.3.1.1.1, Table 26), but also allows (§3.1.3.3.2) for straightforward cases the simpler procedure of taking the coefficients for upwind-face and downwind-face pressures for the basic orthogonal directions of the standard method (direction θ=0o) (§2.4.1, Table 5), and assuming that the upwind-face pressure varies as cos2θ and the downwind-face as cosθ. The resulting forces are combined vectorially (see Note 3 of §3.1.3.3.2). The result is smaller than rigorous application of table 26, but very close to that from the ‘80%’ rule of §2.1.3.6 (above).

When considering the structural stressing at sections significantly above ground level, it should be borne in mind that the static correlation factor (size factor, cs) should reflect the loaded area contributing to the stress in question, not the whole face area. Similarly, the dynamic factor is increased because the dynamic loading is in effect ‘inertial loading’ responsive to the mode shape and thus more intense towards the top. This is not well treated, although the NA does correctly recognise the static correlation (size factor) point – note ad-hoc definition of ‘h’ for table NA3.

There are developed rules in the EN for the treatment of internal pressure (EN7.2.9). The net load for design of the cladding is the net sum of internal and external pressures, but note that this has no effect on the overall loading on the structural frame, and has therefore little impact on this project.

Subjective comfort has been mentioned above. This is a significant design criterion for buildings of this height, and a check based on the codified prediction of alongwind gust response should be undertaken, although you may prefer to make your own deductions from the dynamic factor rather than slavish application of EN B4. In practice, wind tunnel testing would be likely to show the comfort-critical wind action to include a substantial crosswind response component, not treated by B4.