UNIVERSITY OF SOUTH AFRICA

SCHOOL OF ENGINEERING
CONTINUOUS ASSESSMENT

TEST NO: Major Test 1 – Assessment No:3

Semester Course

TST1501

THEORY OF STRUCTURES
Examiner: Ms. MA Rikhotso
Marks: 50 Internal Moderator: Mr. N Matshili
Weight of Assessment: 30% External Moderator:
This test consists of 5 pages. 1 cover page, 1 content page and 3 appendices pages.

INSTRUCTIONS TO ALL STUDENTS:

YOUR SCRIPT MUST BE SAVED WITH STUDENT NO, SUBJECT CODE AND
UPLOADED ON ASSESSMENT PLATFORM.
• Honesty Declaration must be completed
• The module is invigilated
Additional student instructions
1. Students must upload their answer scripts in a single PDF file (answer scripts must
not be password protected or uploaded as “read only” files)
2. NO emailed scripts will be accepted.
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and that the correct answer script file has been uploaded.
4. Students are permitted to resubmit their answer scripts should their initial
submission be unsatisfactory.
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6. Incorrect answer scripts and/or submissions made on unofficial examinations
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opportunity will be granted for resubmission.
7. Mark awarded for incomplete submission will be the student’s final mark. No
opportunity for resubmission will be granted.
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opportunity for resubmission will be granted.
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disciplinary processes.
11. Students suspected of dishonest conduct during the examinations will be
subjected to disciplinary processes. UNISA has a zero tolerance for plagiarism and/or any
other forms of academic dishonesty.
12. Students are provided 30 minutes to submit their answer scripts after the official
examination time. Submissions made after the official examination time will be rejected.
 TST1501
MAJOR TEST 1 2023

QUESTION 1 [25 MARKS]

1.1 A bar of steel, having a rectangular cross-section 8 cm by 4 cm, carries an axial
tensile load of 200 kN. Estimate the decrease in the length of the sides of the cross-
section if Young’s modulus , E, is 200 GN/m2 and poisson’s ratio, v is 0.3. [13]

1.2 For a mild steel rod with a length of 12 meters and a diameter of 16 centimeters,
undergoing an axial force of 40 kilonewtons, and considering a steel modulus of
elasticity (E) of 4x10^5 N/mm^2:

1.2.1 Calculate the stress experienced by the rod. [4]

1.2.2 Determine the strain in the rod. [4]
1.2.3 Find out the elongation of the rod due to the applied force. [4]

QUESTION 2 [25 MARKS]

The Figure 1 below shows a built up section. Calculate the following with XX and YY
as reference point.
2.1 The position of the centroid of the section. [11]
2.2 The second moment of area about the horizontal axis, Ixx. [8]
2.3 The radius of gyration, rx. [3]
2.4 The elastic section modulus. [3]
Y

20 mm

30 mm

30 mm
40 mm
60 mm
10 mm

20 mm

X X
Y Φ20 mm
Figure 1

TOTAL MARKS = 50
©
UNISA 2023

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 TST1501
MAJOR TEST

(FORMULA SHEET)
ANNEXURE A

l  F A
strain ( ) =
F Fl
stress ( ) = ; ;E = = =
A l   l l A l
d 2 bd
A of circle = ; A Aofofrectangle = L=xlxb
rec tan gle b; ; A of triangle =
4 2
M max y
 max =
I

bd 3
Moment of inertia about centroid, I = (rectangle)
12
Ay = A1 y 1 + A2 y 2 ......................

Ax = A1 x 1 + A2 x 2 ..............................
I xx
Moment of inertia, I xx = I GG + Ae2 Radius of gyration, rx =
A

I xx
Elastic modulus, Z ex = Three equilibrium equations: ∑M=0; ∑V=0; ∑H=0
y

M
Slope,  =  EI dx MOHR I

M
Deflection, y =  EI xdx MOHR II

d2y
Mx = EI 2
dx
dy
EI = macaulay' s equation of slope
dx
EIy = macaulay' s equation of deflection

Principal stresses,
1 1
 1, 2 = ( x +  y )  ( x −  y ) 2 + 4 xy
2

2 2
Maximum shearing stress,
1 2 xy
 max = 1 2 ( 1 −  2 ) ;  max =  ( x −  y ) 2 + 4 xy 2 tan 2 =
2  x − y

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 TST1501
MAJOR TEST
PROPERTIES OF PLANE AREAS

TRIANGLE bd
A=
2
d
c=
3
bd 3 db 3
G G Ix = ; Iy =
d 36 36
c 2
bd
Ze =
b 24
d
r=
18
CIRCLE d 2
A= = R 2
4
d
R c=
2
G G d 4 R 4
Ix = Iy = =
d c 64 4
d 3
R 2
Ze = =
32 4
d R
r= =
4 2

RECTANGLE A = bd
d
c=
2
bd 3 db 3
Ix = ; Iy =
12 12
G G 2
bd
d c Ze =
6
d
r=
b 12

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 TST1501
MAJOR TEST
SEMICIRCLE

R 2
A=
2
4R
c=
3
R R 4
G G Ix = Iy =
8
c R
r=
2

©
UNISA 2023

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