Question 1

a) As part of a large structure, the truss structure shown in Figure 5 is designed to support loads at joints D and E. The members will be welded together, in the construction of the structure, to form rigid joints.

(i) Explain briefly why this structure can be modelled as a pin-jointed structure (PJS) for the purpose of determining the forces in the members.

(ii) If A is modelled as a pinned support and B is modelled as a roller support, show that the structure is statically determinate.

(iii) Determine the reaction forces at supports A and B.

(iv) The axial forces in each member are given in Table 1. Using the method of joints, verify that the axial forces in members AC and BC are indeed as given in Table 1. You must show and clearly explain your working.

Figure 5

Table 1 Axial forces in the members

Member       Force/kN

AB                      10.0

AC                      14.0

BC                      -14.1

BD                       -4.0

CD                        6.0

CE                         5.7

DE                       -4.0

b) The structure is to be constructed from steel bars of square cross section with a width of 14mm. The steel has an elastic modulus of 210 GPa and a yield strength of 300MPa. Assess, under the loading shown in Figure 5, whether any of the members in the truss structure is under the risk of failure

by:

(i) yielding,

(ii) buckling.

Show your working and state any assumptions that you make

c) The measurements by the engineers reveal a tensile residual stress of 200MPa in the weldments of the truss structure. They also carry out radiographic inspection and find an edge crack with a depth of 2mm in the weldment of the member AC. Assuming the load in the member is purely axial, assess if the member is under the risk of failure by:

(i) brittle fracture

(ii) plastic collapse

The fracture toughness, KIC, of the steel is 40MPa √m.

Question 2

A vertical axis wind turbine, like the one shown in Figure 2, sits on a post of height 4.0 m. Although the support post is conical, it can be modelled as a hollow cylinder of diameter of 25 cm with a thickness of 1.0 mm. The maximum torque transmitted by the turbine to the post is 100 N m. The proposed material for the post is a steel alloy with density = 7860 kg m-3, shear yield strength 160 MPa and elastic modulus E = 210 GPa. The turbine is designed to withstand gusting storm winds which, with this size of turbine, would produce a horizontal loading of 1000 N. Assuming that the wind load is transferred to the post as a point load at its tip, check the following:

a) If the maximum shear stress in the post exceeds the shear yield strength of

the shaft material.

b) If the end deflection of the shaft in in the wind exceeds 100 mm.

c) The maximum bending moment and its location on the pole.

Question 1

a) As part of a large structure, the truss structure shown in Figure 5 is designed to support loads at joints D and E. The members will be welded together, in the construction of the structure, to form rigid joints.

(i) Explain briefly why this structure can be modelled as a pin-jointed structure (PJS) for the purpose of determining the forces in the members.

(ii) If A is modelled as a pinned support and B is modelled as a roller support, show that the structure is statically determinate.

(iii) Determine the reaction forces at supports A and B.

(iv) The axial forces in each member are given in Table 1. Using the method of joints, verify that the axial forces in members AC and BC are indeed as given in Table 1. You must show and clearly explain your working.

Figure 5

Table 1 Axial forces in the members

Member       Force/kN

AB                      10.0

AC                      14.0

BC                      -14.1

BD                       -4.0

CD                        6.0

CE                         5.7

DE                       -4.0

b) The structure is to be constructed from steel bars of square cross section with a width of 14mm. The steel has an elastic modulus of 210 GPa and a yield strength of 300MPa. Assess, under the loading shown in Figure 5, whether any of the members in the truss structure is under the risk of failure

by:

(i) yielding,

(ii) buckling.

Show your working and state any assumptions that you make

c) The measurements by the engineers reveal a tensile residual stress of 200MPa in the weldments of the truss structure. They also carry out radiographic inspection and find an edge crack with a depth of 2mm in the weldment of the member AC. Assuming the load in the member is purely axial, assess if the member is under the risk of failure by:

(i) brittle fracture

(ii) plastic collapse

The fracture toughness, KIC, of the steel is 40MPa √m.

Question 2

A vertical axis wind turbine, like the one shown in Figure 2, sits on a post of height 4.0 m. Although the support post is conical, it can be modelled as a hollow cylinder of diameter of 25 cm with a thickness of 1.0 mm. The maximum torque transmitted by the turbine to the post is 100 N m. The proposed material for the post is a steel alloy with density = 7860 kg m-3, shear yield strength 160 MPa and elastic modulus E = 210 GPa. The turbine is designed to withstand gusting storm winds which, with this size of turbine, would produce a horizontal loading of 1000 N. Assuming that the wind load is transferred to the post as a point load at its tip, check the following:

a) If the maximum shear stress in the post exceeds the shear yield strength of

the shaft material.

b) If the end deflection of the shaft in in the wind exceeds 100 mm.

c) The maximum bending moment and its location on the pole.

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