代做CIVE2360 Structural Analysis I 2016代写C/C++编程

CIVE2360

Structural Analysis I

January 2016

1. (a) Give your definition of statical and kinematical indeterminacy and state which method you would use to analyse a statically indeterminate sway frame. [5 Marks]

(b) Examine the four planar structures given in Figure 1 and find the degree of statical indeterminacy. Provide an equivalent statically determinate system for all cases. [10 Marks]

(c) Identify the degrees of freedom for all structures in Figure 1 and find what the degree of kinematical indeterminacy is. [10 Marks]

Figure 1

2. (a) The pin-jointed plane truss shown in Figure 2 is pinned at points A and H. The cross-sectional area is for AC, CD, DF, FH 400 mm² and for all other members 200 mm²; all bars are made of steel with Young’s modulus of 200 kN/mm². Determine the reactions at support H. [15 Marks]

(b) Determine the vertical and horizontal deflection at E and D [10 Marks]

Figure 2

3. (a) A symmetric frame. carrying two trusses is loaded as shown in Figure 3.  The structure has roller supports at A and A’, and fixed supports at C, D, C’ and D’.  The joints at B and B’ may be considered rigid and the second moment of area of the horizontal beams is half that of the verticals.  Find the bending moments at all the joints and sketch the bending moment diagram. Assume that the Young’s modulus is constant throughout. [19 Marks]

(b) Calculate the vertical reaction at A and A’ and sketch the deflected shape of the whole structure. [6 Marks]

Figure 3

4. The uniform. beam with nodes A-E, is connected through an internal hinge at point F to beams FG as shown in Figure 4. For the specified loading and noting the cantilevered  section BC:

(a) Determine the bending moments at all the supports and draw the bending moment diagram. [16 Marks]

(b) Calculate the reactions at A and G together with the deflected shape. [9 Marks]

The flexural stiffness EI is throughout 200,000 kNm²

Figure 4

5. (a) Give your definition of ‘principal stresses’. [4 Marks]

(b) A fixed-fixed beam 5m long has a circular cross-section of diameter d=250mm and carries its own weight of 1kN/m plus a triangular distributed downward load of intensity w and a torque at its middle T. A rectangular strain gauge rosette located at a point on the bottom surface of the beam 2m from the fixed end, recorded the following values of strain: ,  and , where the strain gauges ‘a’, ‘b’ and ‘c’ are parallel, at 45^o and at 90^o to the longitudinal axis of the beam, respectively.   If Young’s modulus E is 200kN/mm² and Poisson’s ratio is 0.35, calculate the principal stresses at the point and subsequently the value of w and T. [21 Marks]

Principal strains may be obtained from the rosette strain readings using the following formulae:

Note that for a circular section:

6. (a) State the von Mises and Tresca criteria of elastic failure. Why do we need such criteria in design? [6 Marks]

(b) The propped cantilever beam AB illustrated in Figure 6 has a length of 6m and is made from a circular steel cross-section with radius of 200mm. At its middle it has on one side a 2.5m long lever arm CD made from the same steel section, carrying a uniform. distributed load of w kN/m and on the other side a similar attachment DE though carrying an opposite load. If the stress that causes the breakdown of the section is 250N/mm² determine the maximum value of w according to the von Mises and Tresca theories. Consider for the calculation both the A and D points [19 Marks]

Figure 6