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Assignment No. 1

Assignment No. 1

ENG 1440 Introduction to Statics Mathematical Preliminaries

Date: 2020 09 08 Due Date: 2020 09 16

Question 1: Solve the following simultaneous equations in (i) and determine the determinants in (ii) and (iii). 3 x  6 y  9 z  48 i. 5 x  y  2 z  18 7 x  2 y  4 z  21

5.R1 + 3.R2 & 7.R1 - 3.R3

48.R2 - 33.R3

z=3

y=-1

x=5

3 6 1 ii. 2 5 3 0 3 9 = 3((5*9)-(-3*3)) -6((2*9)-(-3*0)) + ((2*3)-(5*0)) =60

i iii.

j

k

6 3 1.5 200 180 350 = i((1.5*-350)-(-6*180)) –j((3*-350)-(-6*200)) +k((3*180)-(1.5*200)) = 555.0i - 150.0j + 240.0 k

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Assignment No. 1

Question 2:

b

c

A B

C a

For the triangle shown and for the data given, FILL IN THE GAPS USING: -

Graphical solution for problem i, ii & iii(a) Sine and cosine rules for problem iii(b) & iv

Calculate lengths and angles to the nearest 1 decimal. (Show your work on separate sheets of grid paper and state the scale that you have used.)

a (m)

b (m)

c (m)

Ao

Bo

Co

i

12

9.4

4.5

115.0

45

20

ii

6

10.3

9

35.3

84.7

60

iii(a)

12

9

17.1

41.8

30

108.2

iii(b)

12

9

3.7

138.2

30

11.8

iv

6

8

12

26.4

36.3

117.3

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Assignment No. 1

Question 3 5m

5m

5m

3.75 m 3.75 m 3.5 kN

4 kN F

4 kN D

2 kN

G

1.5 kN

B A

H C 7.5 m

E 7.5 m

7.5 m

What is the slope of members BC, CD, DE and EG? Absolute Values: Using similar triangles to determine rise of the members BC 1:1 CD 2:1 DE 1:1 EG 1:1

7.5 m...