THE UNIVERSITY OF AUCKLAND
Multistorey Building Design Midterm Test
Time Allowed: 2.5 Hours
(including time for submission online)
Tuesday, 22 Sept 2020
6:00 – 8:30 pm
Submit on Canvas by 8:30pm – NO EXTENSIONS
NOTE: This is an Open Book exam. Use of programable calculators is permitted.
Answer all THREE questions. All questions are worth 20 marks each, for a total of 60 marks.
In your answers, the source of criteria should be clearly identified unless it is provided in the question. Extracts from design guides and useful equations are given in the APPENDICES Booklet.
Please note that you cannot contact your instructor for clarification on how to interpret the wording. If it appears that some information is missing, make some reasonable assumption to enable you to proceed. All such assumptions must be clearly identified.
In questions requiring calculations, sufficient working and references MUST be given to enable a numerical check to be carried out and FINAL ANSWERS MUST BE CLEARLY IDENTIFIED. Write neatly – you will lose marks for messy answers!
Use calculation software (eg Excel or Mathcad) is acceptable, but should not be required for the problems in this test. You may provide printouts as part of your answer only if all steps of the work are clearly indicated. Spreadsheets where the calculations cannot be followed are not acceptable
You may provide your answers on printout of test paper or on separate pages, but all pages must be clearly numbered, with Surname and ID at the top. Answers may be handwritten or typed. Submit single PDF file with all three questions included.
Academic Honesty Declaration on the next page must be signed and submitted as the front page of your test paper. If not printing the test paper, it must be written in full and signed.
This page must be signed and submitted with your completed test paper
(It can be written out by hand if unable to print.)
Academic Honesty Declaration:
By signing this page and submitting this test, I declare that:
- I have not communicated by any means with anyone else about the test during the test time (6:00-8:30pm, 22 September 2020),
- I have not sought online solutions to the questions,
- I have not reproduced the content of this assessment anywhere in any form, and
- All of the work shown is solely my own.
- Seismic Loading (20 marks)
A heavy single storey, 1-bay reinforced concrete frame building is to be built in Wellington on Class C soil. The beam is infinitely stiff compared to the columns and thus the building has been designed as a “strong-beam-weak-column” mechanism with plastic hinge regions forming at the top of the columns. The columns will be founded on small individual footings.
Key design parameters:
– Z = 0.40
– Ru = 1.0
– N(T,D) = 1
– Sp = 0.7
– m = 4
- columns are 800 mm square (based on preliminary design)
- seismic weight per frame at roof level is W = 3,000 kN
- The inter-storey height is 4 m from ground to the soffit of the beam.
– g=9.81 m/s2
You may assume the following:
- the beam is infinitely stiff and does not yield
- the columns are pinned at ground level
- Find the ULS seismic base shear for the frame, then find the design bending moment at the top of the column. Use a cracked moment of inertia for the columns equal to 0.6Ig. Take Ec = 25,000 MPa. Consider as SDOF. Do NOT use the empirical method based on building height to estimate building period.
- Determine the interstorey drift at ULS (not including P-delta).
(If you have been unable to answer part a, you may assume the ULS base shear is 0.2W –
note this is not the actual answer to part a)
- Use the NZS 1170.5 Method B requirements for P-Delta to estimate the roof P-Delta force. Find the lateral deflection including P-delta and compare the inter-storey drift ratio with the Standard’s limit of 0.025. Note that the kd value for soft storey mechanisms is 1.0.
- Using column interaction diagram in Appendix, select the reinforcement ratio required for the columns to resist the seismic demands (assuming 300E reinforcing steel and a concrete compressive strength of 40 MPa).
- If the columns bases are now assumed to be fully fixed into a substantial foundation beam system, without detailed calculation indicate the likely order of magnitude change in period, base shear, lateral drifts and column bending moments. (Assume km does not change from pin-base system.)
3. Concrete design (20 marks)
The lower floor beam of a 1-bay multi-storey, seismic frame is shown in the Figure below. The beam spans are 12 metres from column centreline to column centreline. Also shown are the bending moment diagrams induced by seismic gravity loads (G & Qu) of 80 kN/m along the beam and due to the earthquake (Eu) design forces. Both sets of bending moments have been found from elastic analyses of the frame. The two columns are 800 mm square and the design yield stress of the reinforcement is 300 MPa and the concrete design compressive strength is 40 MPa.
- Find the elastic design bending moments in the beam for the G & Qu & Eu load case. Your answer should include the bending moments at the column centrelines, column faces, and where the maximum positive moment occurs. Assume that the UDL runs from column centreline to column centreline for simplicity. Redistribute the elastic bending moments to achieve equal peak positive and negative moments. Check that any redistribution of moments does not exceed 30% limit specified in NZS3101.
- The beam is 1000 mm deep by 500 mm wide, reinforced with 6-D32 and 2-D25 bars top and bottom in the section. The centroids of the top and bottom reinforcing can be taken at 100 mm below or above the top or bottom of the section, respectively (see the section sketch). Show that the longitudinal reinforcement is adequate to resist the design bending moments and satisfy the maximum and minimum ductile beam requirements of NZS 3101:2006. The beam reinforcement shown continues over the full span (no laps assumed).
- Select the required spacing of 4-legged R12 tie-sets (fyt = 300 MPa) in the potential plastic hinge regions for shear (no need to check the anti-buckling spacing and restraint criteria of the ties).
- Assuming the total interstorey drift demand at the storey in question is at the NZS 1170.5 limit of 2.5%, determine if the beam satisfies the Kd=19 limit for ductile beams. Assume the plastic hinge length, lp, is half the depth of the beam (i.e. 500 mm).
- Estimate the beam elongation anticipated at this drift demand of 2.5%, based on NZS 3101.
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