Download STL261S Assignment 2 Springs & Thin Cylinders 2021 (1)

ENGINEERING FACULTY
DEPARTMENT OF MECHANICAL ENGINEERING
COURSE:
National Diploma in Mechanical Engineering
(D3MCHE)
SUBJECT:
STRENGTH OF MATERIALS II - STL261S
Assignment 2: Close-coiled helical Springs &
Thin-walled Pressure vessels
DATE:
28 June 2021
DUE DATE:
19 July 2021
WEIGHTING:
10%
EXAMINER:
MODERATOR:
M. LUDICK…………………………………
S. MAKHOMO / W. BOSHOFF…………………….
INSTRUCTIONS
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7.
DOCUMENT TO BE TYPED OR NEATLY HANDWRITTEN.
NO LATE SUBMISSIONS WILL BE ACCEPTED.
DRAW SKETCHES TO ASSIST IN SOLVING THE PROBLEMS.
DRAWINGS MUST BE DONE IN PENCIL.
CALCULATIONS CAN BE TYPED OR HANDWRITTEN NEATLY IN INK
(BLUE \ BLACK) ONLY.
YOU MAY WORK INDIVIDUALLY OR IN GROUPS OF UP TO FIVE (5)
MEMBERS MAXIMUM.
ANY FORM OF COPYING WILL RESULT IN ALL INVOLVED GROUPS
TO GET ZERO MARKS!
SURNAME & INITIALS
STUDENT NUMBER
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STL261S – Assignment 2: Close-coiled helical Springs & Thin-walled
pressure vessels
Question 1
A rigid bar ABCD is pinned at point B and supported by springs at A and D as shown in the
figure below. The springs at A and D have stiffnesses k1 = 10 kN/m and k2 = 25 kN/m,
respectively. If the angle of rotation of the bar due to the action of the load P is limited to 30,
calculate the maximum permissible load Pmax that can be applied.
[10]
Question 2
A safety valve (pressure relieve valve) on top of a pressure vessel containing steam under
pressure p = 2 MPa, has a discharge hole of diameter d = 10 mm as shown in the figure
below. The valve is designed to release the steam when the pressure reaches the maximum
allowable value pmax = 2.23 MPa. If the free height (i.e., uncompressed height) of the spring
hfree = 135 mm and its spring stiffness k = 5 kN/m, what should be the dimension h of the
valve?
[10]
Question 3
A spherical pressure vessel is constructed by bolting two hemispheres together along rigid
flanges as shown in the sketch. The sphere has an internal diameter of 1.5 m and the plate
thickness is 5 mm. Allowable tensile stresses are 45 MPa in the shell and 80 MPa in the bolts.
3.1
3.2
Calculate the allowable gauge pressure.
Determine the number of bolts required if the bolt diameter is 25 mm
(Note: bolt root diameter = 0.84 × nominal bolt diameter)
/2/
/4/
3.3
A thin copper tube, 14 mm internal diameter and 0,5 mm wall thickness has closed
ends and rotates at 1200 r/min while it is subjected to an internal gauge pressure of 222 Pa.
Calculate the total hoop stress in the wall of the tube if the density of copper is 8900 kg/m3.
/4/
[10]
Question 4
A pressurised cylindrical container has a sealed cover plate fastened with steel bolts as
shown below. The internal pressure p in the thin cylinder is 1900 kPa, the inside diameter
D of the cylinder is 250 mm and the diameter db of the bolts is 12 mm.
4.1 If the allowable tensile stress in the bolts is 70 MPa, find the number of bolts needed to
fasten the cover plate.
/3/
4.2 If the diametral change of the cylinder shell is limited to 0,025mm, determine the
thickness of the shell plate required. (ESteel = 200 GPa)
/3/
From the range of sizes given below select the minimum standard thickness of plate to be
purchased for the manufacture of the cylinder.
/1/
8mm; 10mm; 12mm; 16mm; 20mm; 25mm; 30mm; 35mm
4.3 What is the maximum angular velocity in r/min at which the container can be rotated about
a vertical axis through its centre if the maximum allowable tensile stress is limited to 53.5
MPa? The density of steel is 7800 kg/m3.
/3/
[10]
Question 5
The following data refer to two close-coiled helical steel springs.
SPRING
1
2
FREE HEIGHT
55 mm
48 mm
d
4,75 mm
5,3 mm
D
30 mm
44 mm
N
8
6
One spring is placed inside the other, not touching each other, and compressed between a pair
of parallel plates until the distance between the plates is 40 mm. Make a neat detailed sketch
of the spring and plate assembly. If G = 83 GPa for both springs, calculate the following:
5.1 The force applied to the spring assembly.
/4/
5.2 The shear stress induced in each spring.
/3/
5.3 The total strain energy stored in the spring assembly.
/3/
5.4 The stiffness of each spring.
/3/
5.5 The equivalent stiffness of a single spring that can be substituted in place of these
springs.
/2/
[15]
Note: Graduate Attribute one (GA 1) in work schedule
/5/
TOTAL = [60]
STL261S: Springs & Thin cylinders
MARKING CRITERIA – 2021: Assignment 2
Question 1
Pmax
10
Question 2
hvalve
10
Question 3
3.1
3.2
3.3
Pgauge
No. of bolts
Hoop stress
2
4
4
Question 4
4.1
4.2
4.3
5.1
5.2
5.3
5.4
5.5
No. of Bolts
Plate thickness
Standard size
Angular velocity
3
3
1
3
Question 5
Applied Force
Shear stress: Spring 1
Shear stress: Spring 2
Total energy stored
Spring 1 stiffness
Spring 2 stiffness
Equivalent stiffness
4
2
1
3
2
1
2
Graduate Attribute
GA1 Problem solving
TOTAL
%
5
60