Section A – Structural Analysis (95 marks)

Question 1 – Determinate beam (30 marks)

A simply supported beam with two cantilevers either side is subjected to a uniform load of 30 kN/m and a point load of 20 kN as shown in Figure 1. Assume E= 200 GPa and I=120(10)6      mm4

1.1 Calculate the reactions at the supports of the beam                                           (4 marks)

1.2 Draw the shear force and bending moment diagrams with critical values        (12 marks)

1.3 Calculate the deflection at the midspan of beam at F using unit load method  (15 marks)

Fig. 1 Simply supported beam with two overhangs.

Note: The area and centroid of typical shapes used in the unit load method can be found below

Question 2 – Force method (25 marks)

A two-span continuous beam is subjected to both uniformly distributed and point loads as shown in Figure 2. Using the force method, analyse the beam by replacing the support at A by

Fig. 2. Two span continuous beam

Note: The area and centroid of typical shapes used in the unit load method can be found below

Question 3 – Direct stiffness method (30 marks)

A frame structure composed of the girder supported by columns (Note: A and C are fixed,     whilst D is pinned) as shown in Figure 3. The girder BD is subjected to uniformly distributed load with 2kN/m and a concentrated load at E with 16kN. Using the direct stiffness method,  analyse the frame. Assume same young’s modulus for both girder and the columns but          different second moment of inertia (I) values as shown in Figure 3.

Fig. 3. Frame structure.

Question 4 – Shear stress in Beams (10 marks)

The simply supported wood beam in Fig. 4 (a) is fabricated by gluing together three 160-mm by 80-mm plans as shown.

4.1 Calculate the maximum shear stress in the glue                         (5 marks)

4.2 Calculate the maximum shear stress in the wood                       (5 marks)

(a)                                                                     (b)

Fig. 4  A simply supported beam.

Section B – Structural Design (85 marks)

Question 5 – Reinforced concrete beam (35 marks)

A reinforced concrete (RC) slab with a depth of 200 mm is supported by RC beams at a spacing of 4m as shown inFigure1(a). The RC beam is supported by RC columns as shown inFigure  1(b). The cross-section of the RC beam is shown inFigure 1(c). The RC slab has been designed to support a live load of 3.0 kPa and superimposed dead load of 1.0 kPa in addition to its self-

weight. Design the RC beam using the following inputs: RC density = 2,450 kg/m3, f’c = 32 MPa, cover = 30 mm,fy = 500 MPa, ligatures = N10 rebars, reinforcing bar N20, Φ = 0.8.

The following load cases should be considered:  Maximum load intensity = 1.2G + 1.5Q

Minimum load intensity = 0.9G The load cases can be used in combination to obtain critical design actions.

5.1 Calculate the total design load applied to the RC beam                                        (7 marks)

5.2 Calculate design moments at the support A and midspan B of the RC beam       (7 marks)

5.3 Determine the diameter and number of flexural reinforcing bars required for the RC beam at the support section (point A)                                                                              (7 marks)

5.4 Determine the diameter and number of flexural reinforcing bars required for the RC beam at the midspan section (point B)                                                                             (7 marks)

5.5 Sketch two sectional views of the RC beam at points A and B showing the flexural

reinforcing bars                                                                                                       (7 marks)

4m                4m                4m                4m                4m                4m

Reinforced concrete slab                             (a) Plan view

A

(b) Elevation view of beam                            (c) Cross-section of RC beam

Figure 1. Structural system for an office floor

Question 6 – Reinforced concrete column (20 marks)

A reinforced concrete column has six D500N20 bars and N10 ligatures as shown inFigure 2.

Design the RC column using the following input: Density = 2,450 kg/m3,f’c = 32 MPa, cover = 30 mm. The following Φ factors (taken from AS3600) are used:

▪   Φ = 0.65 for a member in axial compression without bending

▪   Φ = 0.85 for a member bending without axial tension or compression

▪   Φ = 0.60 for a member bending with axial compression

6.1 Calculate the axial force ΦNu0 and bending moment ΦMu0                                                  (6 marks)

6.2 Calculate the axial force ΦNub and bending moment ΦMub at a balance point  (10 marks)

6.3 Draw the interaction diagram of the column, and check whether the design action point (N* = 1500 kN, M* = 100 kNm) is located within or beyond the diagram?          (4 marks)

N20 bar

N10 ligature 

          350mm        

350mm

Figure 2. Reinforced concrete column cross-section

Question 7 – Steel beam (30 marks)

The reinforced concrete beam in Question 5 is replaced by a steel beam with universal section 360UB56.7 as shown in

45kN/m

20kN/m

Figure 3. The steel beam is subjected to a uniform load (with self-weight included) as shown

45kN/m

20kN/m

360 UB 56.7

Grade 300

in

Figure 3. The slenderness reduction factor may be taken as 1.0 (as = 1.0) by assuming compact

behaviour. The following inputs can be used:fy = 300 MPa, Φ = 0.9.

7.1 Calculate the design moment, and determine the critical section                         (5 marks)

7.2 Calculate the moment capacity of the beam, and check if the beam can resist the design load or not?                                                                                                           (10 marks)

7.3 Calculate the elastic  section modulus Z with respect to the major axis of the beam. Determine the first yield elastic moment My                                                                                    (10 marks)

7.4 If the section is not compact, which parameters in the design moment equation need to be modified and how to determine them?                                                                   (5 marks)

45kN/m     

20kN/m

A           B

359

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