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Unformatted text preview: Name ______________________________ Student Number ______________________________ DEPT. OF BUILDING, CIVIL & ENVIRONMENTAL ENG.  CONCORDIA UNIVERSITY BCEE 345 – STRUCTURAL DESIGN II (REINFORCED CONCRETE DESIGN) Winter 2005 Dr. K. Galal DURATION OF EXAMINATION: 1:15 to 2:55 pm THIS EXAMINATION PAPER INCLUDES 3 QUESTIONS IN 7 PAGES. YOU ARE RESPONSIBLE FOR ENSURING THAT YOUR COPY OF THE PAPER IS COMPLETE. BRING ANY DISCREPANCY TO THE ATTENTION OF YOUR INVIGILATOR. Special Instructions: 1 This is a CLOSED BOOK exam with the exception that students will be allowed to use an unmarked copy of the design standard CSA A23.3 i.e. brown part of the “Concrete Design Handbook”. The rest of the handbook should not be used. 2 This exam is for a total of 100 points. 3 Attempt ALL THREE questions. 4 The use of any programmable calculator is not allowed. 5 Use information provided. 6 If given data is not sufficient, assume reasonable values for any additional needed information. 7 State clearly all assumptions made. 8 This examination paper must be returned. Design aids: ⎛ 2 K r ⎞ α 1φ c f c′ ⎟ ▪ ρ = ⎜1 − 1 − ⎜ α 1φc f c′ ⎟ φ s f y ⎝ ⎠ φ s ρf y ⎞ ⎛ ▪ K r = φ s ρf y ⎜1 − ⎜ 2φ α f ′ ⎟ ⎟ c 1 c⎠ ⎝ ▪ ▪ ≤ ρ max = α 1 β1φ c f c′ ⎛ 700 ⎜ φ s f y ⎜ 700 + f y ⎝ ⎞ ⎟ ⎟ ⎠ Mr = bd 2 × 10 −6 Kr s ≥ 1.4 db , ≥ 1.4 amax , ≥ 30 mm ▪ min. clear cover to the outside of stirrups: 40mm (Exposed), and 30mm (nonexposed) ∆T ′ ▪ As = φ s f y − φ cα 1 f c′ ▪ ∆T =
M f − M r ( balanced ) d − d′ Continued on page 2 2 Problem 1: [50 points] Figure 1 shows the elevation view of a reinforced concrete beam, which is simply supported with a cantilever. The envelope of the factored moment diagram due to different cases of loading is shown. The beam has a 350x600 mm rectangular crosssection. The compressive strength of concrete is 30 MPa and the reinforcement has a yield strength of 400 MPa. The maximum aggregate size used is 25 mm and the beam is nonexposed. It is required to: [10] 1 Calculate the maximum amount of tension reinforcement (without the use of compression rft.) allowed and the corresponding moment capacity. (Hint: d can be assumed to be 510 mm). [25] 2 Determine the amount of flexural reinforcement required at point B. (exact depth should be used in calculations). [10] 3 Check the minimum steel requirement and minimum bar spacing at point B. [5] 4 Sketch the cross section of the beam at point B and the location of flexure reinforcement along the beam elevation. A B C D 3.0 m 3.0 m 1.5 m 600 350 Crosssection 3.0 m 3.0 m 1.5 m 4.0 m 300 kN.m. Figure 1
0.5 m 650 kN.m. Continued on page 3 3 Continued on page 4 4 Continued on page 5 5 Problem 2: [30 points] For the same beam of Problem 1 and considering a beam depth, d, of 510 mm, it is required to design the vertical stirrups at the critical section corresponding to the largest shear force, using the Simplified Method of CSA A23.394 Cl 11.3. The following figure shows the factored shear force diagram of the beam. The beam is constructed with normal density concrete with fc'=30 MPa. The yield strength of the web reinforcement is 300 MPa. The columns are 400mm x 400mm.
250 kN 100 kN 50 kN 100 kN 100 kN 300 kN 3.0 m 3.0 m 1.5 m Continued on page 6 6 Continued on page 7 7 Problem 3: [20 points] A. Draw a typical strain distribution for a) underreinforced section, b) balanced condition and c) overreinforced section. Indicate maximum strain values for concrete and steel for each case. B. Circle True (T) or False (F) of the following statements: T T T F F F The development length of top bars in beams is more than that of bottom bars. Development length is directly proportional to the concrete compressive strength. For normal strength concrete (2540 MPa) the tensile strength is 2030% of its compressive strength. Hooks may be used to develop bars in compression. If the flexural tension reinforcement bars need to be spliced, in that case it is a good practice to splice all the bars at the location of zero shear. T T F F The End Best wishes
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 Winter '07
 DrGala

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