Trusses and strutures

Please see problems 1,3 of the PDF. Ping only if u can do it now

1

ENGG1802 Assignment 1

Due by 5:00pm Friday 18 October 201

3

(10%)

 You MUST complete these assignment questions independently.

 When you submit your assignment, a statement page with your signature must be attached
to show that “This is my own wor

k

which I was independently completing”.

 Your assignment MUST be in a manila folder or it will not be marked.

 Do not forget writing your student name and SID clearly.

 You must write the tutorial group code you belong to including the name of your tutor
(check these from the course website). Otherwise, a significant delay of returning your

marked assignment may occur.

 You should hand in your assignment to your tutor

OR
 If you are in Stream 1, the assignment is to be submitted to the Assignment box, Level 2 of

the Civil Eng. Building.

 If you are in Stream 2, the assignment is to be put in the Assignment box, Level 3 of the
Mechanical Eng. building.

 NOTE: Late submissions will be penalized 10% of full mark for every day or part thereof

that the assignment is late.

This assignment should take an average student no more than 12 hours to complete.

2

Question 1 (25%):

A crane shown below consists of 2 trusses pivoting at G under the action of a cable J-K-L-M-

N (dashed) to lift a load W supported at point E. Frictionless pulleys at K, L and M all have a

radius of 0.1m.

With the crane in the position shown, the cable is horizontal between attachment point J and

the bottom of the pulley at K, and also between the top of the pulleys at L and M. The cable

travels vertically from the side of the pulley at M to the fixed point on the ground, N. The

cable can support a maximum tension of 40.00kN.

Members forming the stand A-B-D-H-G-C, along with braces A-D, C-D and D-G can

support a maximum tension load of 162.0kN before failing by fracturing, and a maximu

m

compression load of kN where l is the length of the member, before failing by

buckling. All other members can support a maximum tension load of 81.00kN, and a

maximum compression load of kN.

a) Copy and complete the table. Express the tension (or compression) in terms of load W.

b) Find the maximum load W the crane can support. Which member is the limiting member?

c) If the members which support no load are removed, how does the result in b) change?

Section Member Tension (Compression) in terms of

W

l (m)

Cable JKLMN –

S
ta

n
d

AB 3.000

AC 3.000

AD 4.243

BD 3.000

CD 3.000

CG 3.000

DG 4.243

DH 3.000

GH 3.000

B
ra

c
e
GK 2.66

7

HK 1.820

HM 3.162

KM 2.333

B
o
o
m

EF 3.000

EI 3.35

4

FG 3.000

FI 1.500

GI 3.354

GJ 1.500

IJ 3.000

IL 3.354

JL 1.500

3

Hints:





 All angles for the cable are given for the cable wrapped around the pulleys

Figure 1

4

Question 2 (20%):

Figure 2 shows a flyball governor mechanism. The weight of the balls M and N is 6 kg and

the collar CF is 3 kg. The relaxed length of the spring is 0.25 m and its stiffness k is 600 N/m.

Assume the lengths of AB, BC, BM, DE, EF and EN are the same. AD and CF are parallel

and equal, the spring is mounted vertically and attaches at the midpoints.

a) Draw the free body diagrams of the collar CF and the arm ABM
b) Find the force in the strut BC or EF
c) Find the extension of the spring
d) Find the angle of θ as a function of l.
e) Show whether the spring force is dependent on θ to support the collar

Figure 2

5

Question 3 (35%):

There will be a spectacular firework show on Sydney Harbour Bridge that you are planning

to take beautiful photos of. Recently, a camera with a telephoto lens was offered online at a

very special price (shown in Figure 3(a)). Extra care must be taken when using a telephoto

lens mounted on a tripod due to the weight and size of the lens. Without careful positioning,

the tripod may overbalance. The aim of this question is to determine the best mounting

position for the camera-lens system and to investigate other possibilities to make it steadier

on sloping ground. The lens is approximately 500mm long at its minimum focal length and it

can be extended up to 650mm (shown in Figure 3(b)).

The lens has a front and rear section, each with circular cross section which can slide relative

to each other, as shown in Figure 3(c). The rear section, shown in Figure 3(d), has a mass of

4.5kg, whilst the front section, shown in Figure 3(c), has a mass of 1.5kg.

Figure 3(a) Camera with lens attached

showing minimum

extension

Figure 3(b) The lens alone at maximum

extension

Figure 3(c) The front section of the lens

Figure 3(d) The rear section of the lens

Figure 3(e) The front view of the camera

body

Figure 3(f) Section view of the camera

body

6

The camera is approximately 0.9 kg and is simplified into a simple rounded corner bloc

k

with the lens mount at the front and the tripod mount at the bottom.

Calculate the centroid of the lens, the camera and the combined camera-lens system when

the lens is at minimum and maximum extension, relative to the mounting point at the

base of the camera body (see Figure 3(e) and 3(f))

The camera and lens are mounted to a tripod (shown in Figure 3(g)) of mass 2.5kg, using

the mounting point shown in Figure 3(e) and 3(f). The legs of the tripod open to a radius

(AE, BE, CE) of 600mm and the height of the tripod (DE) is 1600mm. The camera must

be mounted such that the lens points along the x-axis between EA and EB. The tripod is

placed on ground sloping at an angle of φ = 3
o
(see Figure 3(h)). Calculate if the system

will tip over when the lens is at its minimum and maximum extension.

The spot for watching the fireworks is very crowded so the tripod leg radius (AE, BE,

CE) must be reduced to 500mm. To maintain balance, additional weight is attached to the

bottom of the tripod head (point D). Calculate the minimum mass required to prevent

tipping when the lens is at its minimum and maximum extension.

Find the minimum mass required if the tripod is moved to other locations with an

inclination angle of 8
o
. The tripod leg radius in this case is 600mm and the lens is at

minimum extension

Figure 3(g) The schematic of the tripod.

Figure 3(h) The tripod-camera-lens system on an incline surface.

7

Question 4 (20%):

As shown in Figure 4(a), a pin connected frame ABC, consists of two rigid bars AB and

BC, of negligible weight, each having a length b = 400 mm. The bars are joined by a

linear spring stiffness k=3 kN/m at their midpoints. Initially, the spring is unstretched, the

framework has a pin support at A, a roller support at C, and is in equilibrium at an angle α

= 45
o
.

The roller support at C is then removed and a block of mass m = 10 kg is placed instead

on an inclined surface β = 5
o
. The static friction coefficient between the floor and the

block is µ = 0.2. A force F = 150 N which is φ = 5
o
to the left from the vertical axis is

now applied on the new structure at joint B, resulting in the block m moving to the right,

stretching the spring. When the system reaches equilibrium, the angle between the bars

and the horizontal will change from α to θ (shown in Figure 4(b)). At this moment:

a) Determine the angle θ after reaching equilibrium (due to space limitation θ must
not be less than 30

o
)

b) Determine the reaction forces at pins A, B and

C

c) What will be the increase in the spring length?

Figure 4(a)

Figure 4(b)

θ θ

β

φ
F

A

C

B

m
k

b/2

b/2 b/2

b/2

α α

A
B
C
k