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CIVE215001 Structural Design
创建日期：2024-09-05 14:46:25
标签： CIVE215001
Structural Design

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CIVE215001

Structural Design 

SECTION A - REINFORCED CONCRETE

1.    Figure 1(a) represents the cross-section of a deep beam that has been cast monolithically with a 1-way spanning slab. In this case, the beam is continuous over 3 spans and each span is equal to 9m. The span of the 1-way spanning slab, which spans between the beams, is 5m.

(a)  Given the following, calculate the effective flange width (beff) of the T-section shown in Figure 1(a) for the first and middle spans.     [6 marks]

beff = (bw  + beff1  + beff2)       where

beff1  = (0.2b1  + 0.1l0) ≤ 0.2l0 ≤ b1 ; beff2  = (0.2b2  + 0.1 l0) ≤ 0.2l0 ≤ b2  (refer to Figure 2 (b))

The beam is subjected to the following loadings:

Permanent action       Gk  = 50.0kN/m (including self weight)

Variable action           Qk  = 35kN/m

Ultimate load               n = 1.25Gk  + 1.5Qk  (maximum) Using the coefficients provided in the Formula Sheet;

(b)  Calculate all of the support moments as well as the maximum span moments in the first and middle span (maximum load is applied to all spans)   [5 marks]

(c)  Determine the areas of reinforcement required in the first span and at the first internal support (NOT the end support) based on the beam cross-section shown in Figure  1(a) and the moments calculated in b) above. Sketch the cross-sections making sure that you adhere to the basic detailing rules.   [12 marks]

(d)  If the load pattern applied to this 3-span beam was ‘Maximum: Minimum: Maximum’, sketch the deflected shape for the 3-span beam. What type of moment could potentially occur at the mid-span of the middle span?   [2 marks]


2.    (a)     For ultimate limit state design, the design strength of concrete in compression is taken to be 0.85fck  / Yc, where Yc  = 1.5. Suggest two reasons for us needing Yc  (use a sketch to illustrate your answer).

Suggest two factors for which the 0.85 reduction coefficient takes account of? Use sketches to illustrate your answers.    [4 marks]

(b)     For reinforcement Ys  = 1.15.   Why is the design strength of steel taken to be

fyk / Ys?                                                                    [1 mark]

(c)    Assuming normal (Gaussian) distribution, sketch the graph for:  Number of Test Results versus Concrete Compressive Strength. Indicate mean strength and characteristic strength. What percentage of results should fall above the characteristic strength (defined as mean strength – 1.64 standard deviation)?    [4 marks]

(d)    YG = 1.35 for permanent actions and YQ  = 1.5 for variable actions

Why do we apply aY factor to the permanent and variable actions and why are they different values?             [2 marks]

(e)     For a singly reinforced rectangular sagging concrete beam subject to bending moments, various criteria apply when designing for Ultimate Limit State. For abeam of effective depth d and with tensile reinforcement of area As, explain why the following requirements need to be applied:-

Why is a minimum percentage area of tensile reinforcement required?

Give two reasons for limiting the maximum value of the lever arm, z to 0.95d.   [4 marks]

(f)   Provided the applied ultimate bending moments are not redistributed, for a truly balanced section, the concrete, at the position where the beam is sagging, reaches its theoretical failure  strain  ( εc   = 0.0035 )  at  the top of the beam at the same  time  that  the  tension reinforcement reaches its yield strain, εy= 0.00217,            determine x/d for this case.   [4 marks]

(g)  For a singly reinforced rectangular concrete beam in bending, sketch the strain and stress profiles for the following three cases as the moment increases from zero to failure:-

(i)       low moment – uncracked section

(ii)      working/serviceability moment-cracked section

(iii)     initial yield of reinforcement

Show the variation in the depth of neutral axis and give approximate values of stress and strain. All diagrams should be to the same scale in terms of order of magnitude.     [6 marks]


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