Q1

 

A simply supported beam has a concentrated downward force P

at a distance of a from the left support, as shown in the figure

below. The flexural rigidity EI is constant. Find the equation of the

Elastic Curve by successive integration.

 

[5 Marks]

 

Q2

 

Determine the rotations at A and B due to an applied moment MB

on the beam, as shown in the figure below. Use the Method of

Virtual Work.

 

[4 Marks]

 

#

Q3

 

Find the strain energy stored per unit volume for the materials

listed below when they are axially stressed to their respective

proportional limits.

 

[3 Marks]

 

Material

 

Proportional

Limit (N/mm2)

 

Mild Steel

Aluminium

Rubber

 

247

412

2.06

 

Modulus of Elasticity

Proportional Limit

(N/mm2)

2.06 x 105

7.20 x 104

2.06

 

Q4

 

As shown in the figure below, find the downward deflection of the

end C caused by the applied force of 2 kN in the structure.

Neglect deflection caused by shear. Let E = 7 x 107 kN/m 2.

 

[5

Marks]

 

Q5

 

For the loaded beam, as shown in the figure below, determine the

magnitude of the counter weight Q for which the maximum

absolute value of the bending moment is as small as possible. If

this beam section is 150 mm x 200mm, determine the maximum

bending stress. Neglect the weight of the beam.

 

[5 Marks]

 

Q6

 

A wooden beam with sectional dimensions of 150 mm x 300 mm,

carries the loading as shown in the figure below. Determine the

maximum shearing and bending stress for the beam.

 

[6 Marks]

 

Q7

 

For the box beam shown in the figure below, determine the

maximum intensity w of the distributed loading that can be safely

supported if the permissible stresses in bending and shear are 10

N/mm2 and 0.75 N/mm2 respectively.

 

[5 Marks]

 

Q8

 

A beam of rectangular section 450 mm wide and 750 mm deep has

a span of 6 metres. The beam is subjected to a uniformly distributed

load of 20 kN per metre run (including the self-weight of the beam)

over the whole span. The beam is also subjected to a longitudinal

axial compressive load of 1500 kN. Find the extreme fibre stresses

at the middle section span.

 

[5 Marks]

 

Q9

 

A hollow alloy tube 5 metres long with external and internal

diameters equal to 40 mm and 25 mm respectively, was found to

extend by 6.4 mm under a tensile load of 60 kN. Find the buckling

load for the tube when it is used as a column with both ends

pinned. Also find the safe compressive load for the tube with a

Factor of Safety of 4.

 

[4 Marks]

 

Q10

 

A cantilever beam of length l carrying a distributed load varies

uniformly from zero at the free end to w per unit run at the fixed

end. Find the slope and downward deflection of the free end B.

 

[8 Marks]

ComputerScienceExpert

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Status NEW Posted 21 Apr 2017 04:04 AM My Price 12.00

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