assignment 1

ENSC 3004 SOLID MECHANICS

ASSIGNMENT 1

1. EXPLAIN WHAT THE OUTRIGGERS ARE USED FOR IN TAIPEI TOWER

Outriggers are there to stabilise the Taipei Tower, in the event of strong forces that act

against the tower such as winds, it stops the tower from moving.

2. HOW MANY OUTRIGGERS ARE ON THE FLOOR IN WHICH THEY ARE USED?

There are eight outriggers on the floor.

3. SKETCH THEIR POSITION ON THE FLOOR. SHOW THE CORE STRUCTURE AS WELL

4. KNOWING THAT P=160 KN, DETERMINE THE AVERAGE NORMAL STRESS AT THE MIDSECTION

OF

A) ROD AB

B)

C) ROD BC

A) P= 160000 (N) => Tension

AAB

= 1963.4954 mm2

AB =


ASSIGNMENT 1

B) F= 160000 N 2*120000 N => F= -80000 N = 80000 N (Compression)

ABC

= 4417.8647 mm2

BC =

5.

6. THE RIGID BAR EFG IS SUPPORTED BY THE TRUSS SYSTEM SHOWN. KNOWING THAT THE

MEMBER CG IS A SOLID CIRCULAR ROD OF 18 mm DIAMETER, DETERMINE THE NORMAL

STRESS IN CG.

Using portion EFCB as a free body

+ FY =0 =

Using beam EFG as a free body

FCG

G F

C B

FDE

FAE

FAB

15000 N

E

G F

FCF

FBF

FDE

FAE

15000 N

E


ASSIGNMENT 1

+ MF = 0 = -1.2m

Cross sectional area of member CG

ACG

= 254.469 mm2

Normal stress in CG

CG =

7. WHEN THE FORCE P REACHED 8 KN, THE WOODEN SPECIMEN SHOWN FAILED IN SHEAR

ALONG THE SURFACE INDICATED BY THE DASHED LINE. DETERMINE THE AVERAGE

SHEARING STRESS ALONG THAT SURFACE AT THE TIME OF FAILURE.

Area being sheared

A= 90 mm *15 mm = 1350

Force P = 8000 N

Average Shearing stress

=

8. FOR THE ASSEMBLY AND LOADING SHOWN. EACH OF THE FOUR LINKS HAS AN 8 X 36 mm

UNIFORM RECTANGULAR CROSS-SECTION AND EACH OF THE FOUR PINS HAS A 16 mm

DIAMETER.


ASSIGNMENT 1

DETERMINE

A) The average shear stress in the pin at B

+ MC = 0 = 0.4m

=

Thus,

B) The average bearing stress at B in member BD

A= dt = (16mm)*(8mm) = 128 mm2

BD =

C) The average bearing stress at B in member ABC, knowing that this member has a 10 X 50

mm uniform rectangular cross-section

A= dt = (16mm)*(10mm) = 160 mm2

B =

C B

FBD

20 KN

A

FCE


ASSIGNMENT 1

9. THE SAMPLE IS COMPRESSED BY AXIAL LOADS p AND q AS SHOWN IN THE FIGURE. WRITE

DOWN THE STRESS STATE IN THE COORDINATE SYSTEM X1X2X3 SHOWN IN THE FIGURE. FIND

THE STRESS ON THE PLANE INCLINED TO THE HORIZONTAL PLANE X1X2. SHOW THE

COMPONENTS OF STRESS ACTING ON THE VOLUME ELEMENT ALIGNED WITH THE INCLINED

PLANE.

p= 10 MPa

q= 20 MPa

ANGLE 40 X1 X2 X3

X1 1 0 0

X2 0 0.766 0.643

X3 0 -0.643 0.766

Rotation Matrix

[A] =[

]

= AAT

= [

] [

] [

]

=[

]


ASSIGNMENT 1

10. THE WOODEN MEMBERS OF UNIFORM RECTANGULAR CROSS SECTION ARE JOINED BY THE

SIMPLE GLUED SCARF SPLICE SHOWN. KNOWING THAT THE MAXIMUM ALLOWABLE

SHEARING STRESS IN THE GLUED SPLICE IS 620 KPa

DETERMINE

A) The largest load P that can be safely applied

= 90 - 45 = 45

A = (150 mm)*(75 mm) = 11250 mm2

20 MPa

14.137 MPa

15.869 MPa

X1


ASSIGNMENT 1

B) The corresponding tensile stress in the splice

=

11. TWO STEEL PLATES ARE TO BE HELD TOGETHER BY MEANS OF 16-mm DIAMETER HIGH-

STRENGH STEEL BOLTS FITTING SNUGLY INSIDE CYLINDRICAL BRASS SPACERS. KNOWING

THAT THE AVERAGE NORMAL STRESS NUST NO EXCEED 200 MPa IN THE BOLTS AND 130

MPa IN THE SPACER. DETERMINE THE OUTER DIAMETER OF THE SPACERS THAT YIELDS THE

MORE ECONOMICAL AND SAFE DESIGN.

Pb = Ps

For the bolt

b =

For the spacer

s =

Equating

Pb = Ps

+


ASSIGNMENT 1

REFLECTION/ FEEDBACK

We got to know the members of the group while we were in the tutorial time and we have

enjoyed working together so far. We discuss and we agreed that the unit as a whole has

been an excellent opportunity to increase our knowledge. To stand out, the tutor has been a

good support when doubts appeared.

assignment 1

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