Q1 determine the magnitudes of the forces in members a b c

Question

1 Structures:

Q1. Determine the magnitudes of the forces in members a, b, c in the simplest possible way.

Q2. A concrete road bridge is proposed to have the profile shown below. Indicate with diagrams how you might prestress this. Provide in  your answer a list of the factors influencing your decisions

2 Fluid Mechanics

Q3. (a) A wide rectangular channel has a slope S = 0.02. The bed and walls of the channel are paved with concrete. The value of Mannings roughness coefficient is n = 0.014 and the discharge per unit width of the channel is q = 3m²/s. Specify if the flow in the channel is sub- or supercritical and find the depth and velocity of the flow.

(b) The flow from the channel enters a natural channel of a similar cross-section. A downstream control is used to maintain the depth H = 1.2m just upstream of the entry point (see figure). To prevent the erosion of the natural bed a horizontal apron is used. Estimate the minimal required length of the apron L to ensure that the hydraulic jump occurs over the paved surface.

Q4. A mooring tower used for loading oil onto tankers at an offshore oil field comprises a vertical circular sectioned steel tower 7m in diameter. The water depth is 100m and the tower is kept vertical by means of 4 guy cables attached to the tower at a height of 70m above the seabed. These cables are anchored to the bed at the four comers of a square which is centred on the tower and has a diagonal length of 140m.

Local tidal currents have a maximum velocity of 1.2m/s at the water surface and reduce approximately linearly to the value of 0.2 m/s just above the seabed at the

base of the tower. Estimate the maximum tension the guy cables have to withstand due to this tidal current.

Also calculate the horizontal reaction force at the tower base to satisfy overall equilibrium conditions.

The following data should be used in your calculation: for seawater µ = 1.5 × 10^-3 kg m^-1s ^-1 and ρ = 1025 kg/m³; for a circular cylinder, CD = 1.2 for Reynolds number Red < 3 × 10⁵ and CD = 0.6 for Re > 3 × 10⁵.

3 Materials

Q5. Discuss the advantages and disadvantages of using each of the Portland cements whose oxide composition and compressive strength properties are given in the table below for:

(a) Precast pretensioned concrete beams in which a concrete compressive strength of 30MPa at three days is required for the transfer of the prestress.

(b) A 15 m×8 m×5 m deep foundation of a cable stayed bridge in which concrete of strength class C25/30 (BS EN 206) has been specified, and the sulfate content of the groundwater in contact with the foundation is 6.5 gms/litre.

Q6. (a) It is often stated that the toughness of structural material is defined as the area under the stress/strain graph. Explain carefully why this is not strictly true.

(b) Explain why toughness is an important property for structural materials.

(c) Describe and discuss a method of increasing the toughness of concrete.

4 Soil Mechanics

Q7. (a) Show how in clay peak states depend on stress level and overconsolidation ratio.

(b) Table 1 gives results from triaxial tests on two samples of clay. Samples A and B were compressed isotropically to reach normally consolidated states at mean effective stresses p′ = 200kPa and p′ = 400kPa respectively. They were then sheared drained at constant cell pressure. The specific volumes of the samples at the start of shearing were recorded to be 1.99 for sample A, and 1.90 for sample B.

Determine the critical state parameters (M, Γ, λ) for the clay

(c) A third sample C was tested in the triaxial apparatus. Sample C was compressed isotropically to reach a normally consolidated state at p′ = 200kPa with a specific volume v = 1.99, and was then sheared undrained.

Determine the final stress state (p′, q′) and final pore water pressure in the sample. You will assume that the pore water pressure at the start of shearing was equal to zero.

Q8. A flexible square footing, 4m wide, applies a stress of 80kPa to a very deep layer of clay. The shear modulus G of the clay has been determined as 15MPa.

(a) Draw a profile of the immediate settlement for a section running from the centre of the footing diagonally to one corner of the square. What is the area of most serious differential settlement?

(b) Calculate the consolidation under the centre of the foundation, demonstrating that below 10m depth the contribution to that settlement is negligible. The coefficient of compressibility mv is 0.4m2/MN at the surface, decreasing linearly with depth to 0.1m2/MN at 10m. You may use a value of A = 0.4 to apply Skempton & Bjerrums correction. It is assumed that the influence factors to calculate stresses under a square footing are equal to those under a circular footing of same area. Relevant tables and charts for the influence factors are given in the Appendix.

Influence factors for rectangular loading: corner settlement

Elastic stress distribution below centre of uniform circular and strip loading

Answer 1

In order to answer the following questions, apply the appropriate principles and concepts and respond accordingly. Q1. Find out the magnitudes of the forces in members a, b, c in the simplest possible manner. Q2. A concrete road bridge is recommended to encompass the profile illustrated below. Point out with diagrams how you might prestress this. Give your answer as a list of the factors affecting your decisions. Q3. Illustrate the merits and demerits of using each of the Portland cements whose oxide composition and compressive strength properties are provided in the table illustrated: a) Precast pretensioned concrete beams in which a concrete compressive strength of 30MPa at 3 days needed for the transfer of prestress. b) A 15 m x 8 m x 5 m deep base of a cable stayed bridge in which concrete of strength class C25/30 (BS EN 206) has been specified, and the sulphate content of the groundwater in contact by the foundation is 6.5 gms/litre.