### Task

### Assignment 1: Concept design, computational modelling, analysis and design.

Prepare a design appraisal with appropriate sketches indicating between three to four distinct and viable structural options for the proposed building structure. The design options should include two structural grids (shown in Figures 1 and 2) for positions of columns and primary beams and justifiable flooring layouts (e.g. 1 and 2.5 m joist spacing). Alternate joist orientation may be adopted so that the distribution of the gravity loading to the primary beams takes place in a uniform manner for rationalisation purposes.

Make a full computational model (using SAP2000) of the whole structural system including beams, columns and joists. Then:

1. Apply gravity loading of Permanent (Dead) and Variable (Live) actions as separate load patterns on the flooring areas. Add the permanent UDL from external walls directly to the perimeter beams. Self-weight of the structure is accounted for in the computational model.

Define the lateral wind loading parameters according to EN1991-1-4 based on a UK location.

2. Assume rigid beam-to-column joints for moment frame structural system in both directions and simply supported flooring joists.

3. Assume preliminary standard UKB for primary beams and joists and square hollow section (SHHF) for column members. Class 4 sections should be avoided for columns (i.e. the width/thickness ratios of the section sides should be less than 34 for S355 steel grade). For the designs where the smallest available UKB results in underutilised flooring joists or beams, the joist spacing may be increased.

No need to incorporate the staircase elements and the lift in the computational simulation. Both are assumed with a separate structure so there is no imposed load to the main structure.

4 Run the analysis and check the deformed shapes under gravity and lateral loads for all the design options.

1. Ultimate Limit State (ULS). Design primary beams, joists and columns using Eurocode 3. Start with the model proposed design using Auto Select list. Refine your design by grouping of the members for practical purposes considering limited rationalisation in favour of maximum optimisation. The final design should include minimum number of overdesigned members (i.e. with utilisation ratios, also called the demand to capacity ratios (DCRs), being less than 0.7) considering reasonable number of grouped members. No composite action is assumed for the design of the beams and flooring joists.

2. Serviceability Limit State (SLS). Check the relative lateral deformations of the floors not exceeding the limit of storey height/250 and the vertical deformations of the beams and joists under dead and live loads are less than the span/360. It is assumed that pre-cambers are not used for permanent loads. If necessary, the designed sections based on ULS should be increased to satisfy the SLS requirements.

Report on all your final ULS and SLS design outputs. Show both the designed sections and DCRs for all the plans and elevations for ULS (using Design tab…Display Design info…) as well as vertical and lateral deformation contours for SLS.

3. Compare and discuss different designs and choose the one with minimum whole-life carbon complying with the European average EPD (kg CO2e/kg) (based on the total weight of beams, columns and floor joists). Use tabulated list of sections and the total weight for each design option (using Display…Show Tables…Miscellaneous Data…Material List…By Section Property).

### Assignment 2: Class 4 joisted floor design.

For the design option with minimum whole-life carbon in Assignment 1, design an alternative joisted flooring system for all the levels using Class 4 I-sections (i.e. the design strength should be governed by local buckling) with a constraint on the maximum web depth of 350 mm and minimum DCR of 0.7.

1. Report the full hand calculations of the final design as follows:

Based on EN 1993-1-5, calculate

a) the effective width of the flange.

b) the stress ratio (factor) of the web accounting for the effective flange width.

c) the effective height of the web.

b) the stress ratio (factor) of the web accounting for the effective flange width.

c) the effective height of the web.

Based on the effective cross section calculated above, determine

d) the location of the neutral axis.

e) the magnitude of the maximum section modulus, Weff, of the effective cross section. Perform iterative calculations if needed.

f) Check the maximum bending moment for the joist against Mc,Rd.

g) Check the maximum deflection to be less than the limit of span/360 under live loads.

e) the magnitude of the maximum section modulus, Weff, of the effective cross section. Perform iterative calculations if needed.

f) Check the maximum bending moment for the joist against Mc,Rd.

g) Check the maximum deflection to be less than the limit of span/360 under live loads.

The maximum bending moment of the flooring joists can be extracted from the computational model in Assignment 1 using summary report in the design stage.

Alternatively, you may calculate the maximum bending moments based on the load sharing of the joists. The load combinations should be adopted according to Eurocode BS EN 1990.

2. Compare and discuss the results for the whole-life carbon between the Class 4 and the UKB joisted floors.

Note: A spreadsheet calculation is provided (in MyAberdeen) to facilitate the design iteration in favour of an optimised final design with less use of steel.

### Assignment 3: Stiffness method.

Extract an arbitrary portal frame, schematically shown in Fig. 3, from the ground floor level of the final design in Assignment 1. Approximate the share of wind loading resisting by the chosen portal frame as well as the share of floor dead and live loading applied in horizontal

and vertical directions, respectively.

and vertical directions, respectively.

### Using the stiffness method:

1. Determine the horizontal deflection of the portal frame subject to the applied horizontal and vertical loading using the designed sections in Assignment 1.

2. Compare the calculated horizontal deflection with that of the computationaal analysis in Assignment 1 and discuss the difference.

3. Make a 2D computational model of the chosen portal frame and apply the approximated horizontal and vertical loads. Run the analysis and compare the horizontal deflection with that of the hand calculation above.

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