assignment 1
DESCRIPTION
solid mechanicsTRANSCRIPT
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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 =
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ENSC 3004 SOLID MECHANICS
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
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ENSC 3004 SOLID MECHANICS
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.
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ENSC 3004 SOLID MECHANICS
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
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ENSC 3004 SOLID MECHANICS
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
= [
] [
] [
]
=[
]
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ENSC 3004 SOLID MECHANICS
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
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ENSC 3004 SOLID MECHANICS
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
+
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ENSC 3004 SOLID MECHANICS
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.