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Examinations:Semester: 1 2004Paper 1 of 1

School of Engineering & Science Campus : Hawthorn

Subject Code(s): HES 2120

Full Subject Title: STRUCTURAL MECHANICS

STUDENT’S NAME: _________________________________ID No: ________________

Duration: 180 minutesPercentage of overall assessment

covered by this paper : 75 %

Reading Time: 15 minutes

INSTRUCTIONS TO CANDIDATES

Materials Allowed

Answering Requirements

Answer all questions, state formulae used.

Swinburne University of Technology

School of Engineering AND SCIENCE

FINAL EXAMINATION - 1 st Semester 2004

(HES 2120, Structural Mechanics)

QUESTION ONE

An electric motor exerts a torque of 800 Nm on the rotating steel shaft ABCD shown, there is a bearing at D. The diameter of the shaft must be uniform throughout and there are two further design requirements : - the angle of twist between A and C must not exceed 1.5o; - the maximum permissible shaft shear stress is (MAX = 60 MPa. Determine the minimum shaft diameter that may be used, G = 77 GPa. (16 marks)

[pic]

Fig. 1

QUESTION TWO

A composite bar is made by securely bonding an aluminium strip (EA = 70 GPa) to a copper strip (EC = 105 GPa) as shown. The composite bar is bent about a horizontal axis with a moment of 30 Nm. Determine :

a) Location of centroid for transformed section, [pic]; and corresponding centroidal moment of inertia, IX . b) Maximum stress in aluminium strip.

c) Maximum stress in copper strip.

(18 marks)

[pic]

Fig. 2

QUESTION THREE

Member AB is a steel column of length 2.5 m for which E = 200 GPa and IX = 3.25 x 105 mm4. At the point in erection when ( = 300 the load is as shown, pins at A and B pass through the column centroid. Determine the factor of safety against Euler buckling of the column. Motion is constrained to the plane. (12 marks)

[pic]

Fig. 3

QUESTION FOUR

The figure below shows the state of stress in a surface element for a material subject to plane stress ((z = 0). Determine the following : (Note : Your answer must include a sketch of the relevant Mohr’s circles.)

a) Maximum and minimum principal in-plane normal stresses b) Orientation of principal planes.

c) Maximum in-plane shear stress.

d) Maximum out-of-plane shear stress.

(17 marks)

[pic]

Fig. 4

QUESTION FIVE

A cylindrical pressure vessel of 250 mm mean diameter and 6 mm wall thickness is fabricated from a 1.2 m length of spirally welded pipe AB as shown. Tank gauge pressure is 4 MPa and centric axial forces P and P1 of 240 kN act through rigid end plates. Determine : a) Net longitudinal and hoop stresses.

b) Normal stress acting perpendicular to weld and shear stress parallel to weld (show sketch of Mohr’s circle). c) Determine the Factor of Safety which exists according to the distortion energy theorem, if the material is steel with a yield stress (Y = 300 MPa.

(17 marks)

[pic]

Fig. 5

QUESTION SIX

A simply supported beam ACB has a point load and a U.D.L. applied as shown. Determine :

a) Reactions at A and B.

b) Equations for shear force and bending moment for the whole beam. c) Using Macauley’s double-integration method, determine the equations for slope and deflection. Take EI = a constant. (20 marks) [pic]

Fig. 6

FORMULAE :

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(A2 - (A .(B + (B2 = ((Y /...

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