Lecture notes for theme 1 of Statics. Contains all calculations for the theme so you can pay attention to explanations in lectures in stead of scrambling to write down notes because they aren't released. I made these notes during my first year of Mechanical engineering at the University of Pretoria...
Consider a general triangle with the following representation.
θ Determine the remaining three unknowns in each of the fol-
lowing situations.
b
a 1. a = 2, b = 3, θ = 60◦ .
α 2. c = 6, α = 60◦ , β = 10◦ .
β
c 3. b = 3, c = 4, θ = 30◦ .
4. a = 5, b = 2, β = 15◦ .
NOTE: We will use the following accuracy for numerical values.
• If a specific scalar (excluding an angle) is used in a next step of your calculation, use at
least 4 significant figures.
* You may use a representation with more significant figures.
* A representation with less than 4 significant figures is not allowed, as it decreases
on the accuracy of your final answers.
• If an angle is used in a next step of your calculation, use at least a 1 decimal digit
representation.
* You may use a representation with more decimal digits.
* A representation with less than 1 decimal digit is not allowed, as it decreases on
the accuracy of your final answers.
• Represent all final answers to exactly 4 significant figures, except for angles.
• Represent all final angles to exactly 1 decimal digit.
EXAMPLE: If you have to use the value of π = 3.14159265..... in a follow-up calculation,
you may use the built-in calculator value of π.
You may also use the values 3.142, 3.1416, 3.14159, etc.
The values 3, 3.1 and 3.14 do not meet the required accuracy and are not used in follow-up
calculations.
If you have to represent π as a final answer, you will represent it as 3.142.
1
in notes
,Lecture Unit 1.2
Question 1
Consider the structure in the accompanying sketch that is subjected to the given horizontal
and vertical forces at A. B and C are pin connections in the same plane; the distance between
the two points is variable.
6m
600 kN
450 kN A
B 30° C
Our aim in this problem is to see how the resultant force at A is distributed between the
connecting members AB and AC under specified circumstances. This is equivalent to finding
components along specified directions.
1.1 Determine the magnitude R of the resultant R of the 450 kN and 600 kN force and
specify the direction of R.
1.2 Calculate the components of R along the members in the following circumstances and
interpret your results graphically.
(a) Member AB is vertical. Calculate the components along AB and AC.
(b) Member AB has a length of 5 m. Calculate the components along AB and AC.
(c) Member AB is vertical; a third member is connected from A to the midpoint of B
and C, call this point D. Calculate the components along AB, AD and AC.
1.3 What conclusions can you draw from your answers in Question 1.2?
2
In notes
,Question 2
arctan E
The force system on the hook consists
of three forces. Two forces are known
completely (the magnitudes and direc-
tions are known) and a third force is
unknown in terms of both its magni-
u tude and direction.
Answer the following questions and
measure θ as an angle anticlockwise
from the positive x−axis.
2.1 Determine the magnitude and direction of the smallest force F so that the resultant of
all three forces has magnitude 600 N .
2.2 Determine the magnitude and direction of the largest force F so that the resultant of
all three forces has magnitude 600 N .
2.3 Determine the magnitude and direction of the smallest force F so that the resultant of
all three forces has magnitude 500 N .
2.4 Determine the magnitude and direction of the largest force F so that the resultant of
all three forces has magnitude 500 N .
Circle method
SMALLEST
F
LARGEST F
R
F
E
R E
F R T FRIT
3
, 325N
i
g
β 45 arctan 112.38
R 3252 6002 21325600 05 180_B
By s Oβ
32.25
I FR I 600N
I
E R
GOON For
or
BUT FOR SMALLEST F LARGEST
R
Tp E
F
F R T F RIT
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