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.

 

 

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.

Attachments:

• 1492665044-flexural rigidity.docx