TAXATION NOTES FOR A LEVEL STUDENTS OFFERING ECONOMICS OR ENTRENEURSHIPFull description
Module 1
Physics 2 - Module 1
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JanaBabes
course outline for taxation 1Full description
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control engineering
Curso de feng shui
SS,Speed Seduction, NLP, Ross Jeffries
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Room 206 JPD Building 1955 CM Recto Avenue, Manila Telepone !um"e#$ %02& 516 '559 ()Mail$ mega#evie*+200 mega#evie* +200 -.aoo/com
Review M7D;( M7D;( 1 TR(!
strength strength of of materials materials.. The The stress stress in any member under loading is: σ =
P A
where:
σ
3t#e33
P 4o#ce
% punch for ma+ing holes in steel plates is shown in the figure. %ssume that a punch having diameter d ' *)mm is used to punch a hole in an 7mm plate. If force P ' $$) 89 is reuired to create a hole
A a#ea
!o#mal t#e33 t#e33 - either tensile or compressive stress produced by force acting perpendicular to the area. ea#ing ea#ing t#e33 t#e33 – is produced produced whenev whenever er the applied applied load load causes sliding to to the sections. It is either a single shear or double shear. Bea#ing t#e33 – is th the contact pressure between separate bodies. PRO!"# $ % hollow circular post %& supports a load P $ ' $()) lb acting at the top. % second load P * is uniformly distributed around the cap plate at . The diameters and thic+nesses of the upper and lower parts of the post are d % ' $.*, in. t % ' )., in . d& ' *.*, i n. and t&' ).(, in. espectively/ r espectively
a. b. c.
PRO!"# 3 Two plates upper plate $,mm thic+ and lower plate $)mm thic+ ar =oined by four rivets rivets of *) mm diameter as shown. shown. %ssume %ssume the load is eually divided among the rivets.
a. b. c. a. b.
c.
&alculate &alculate the normal normal stress stress in the the upper upper part part of the the post. post. If it is desi desire red d that that the lowe lowerr part part of the post post have have the the same same compress compressive ive stress as the upper part what should be the magnitude of load P *. If P $ remains at $()) lb and P * is now set at **/) lb what new thic+ness of & will result in the same compressive stress in both parts.
PRO!"# * %n ! – shaped concrete concrete slab $* ft 0 $* ft 1but with a / ft 0 / ft cutout2 cutout2 and thic+ness t ' 3 in. is lifted by three cables attached at O and 4 as shown in the figure. The cables are combined at point 5 which is (.) ft above the top of the slab and directly above the center of mass at &. "ach cable has an effective cross sectional area of ).$/ in *.
a. b.
6ind 6ind the the tensil tensile e forc force e in in each each cable. cable. 6ind 6ind the the avera average ge stress stress in each each cable. cable.
PRO!"#
;hat ;hat is the the avera average ge shea shearr stres stress s in the the plate plate< < ;hat ;hat is the the averag average e compre compressi ssive ve stres stress s in the punc punch< h< ;hat ;hat is the the avera average ge bear bearing ing str stress ess in in the the plate< plate<
d.
&alcul &alculate ate load load P that that can can be applie applied d if the shea shearin ring g stress stress in in the rivets is limited to 7) #Pa. &alculate &alculate load load P that can be applied applied if the the bearing bearing stres stress s in the the plates is limited to $3) #Pa. &alcul &alculate ate load load P that that can can be applied applied if the the tensil tensile e stress stress in the the rivets is limited to $)) #Pa. ;hat is the ma0imum safe load P<.
D(7RMAT87! 7 M(MB(R !D(R A:8A; ;7AD8!< PL AE
where:
a=ial de4o#mation
P a=ial 4o#ce A con3tant c#o33 3ectional a#ea ; lengt ( Modulu3 o4 (la3ticit. PRO!"# , 1*, points2 The rigid bars %& and "6> are supported by pins at & and >. The vertical rods are made of aluminum with stress strain diagram shown and bron?e with properties given. a. &ompute &ompute the stressa stressand nd elongation elongation in the aluminum aluminum rod. b. &omput &ompute e the stress stress and and elong elongati ation on in the the bron? bron?e e rod. rod. c. &alculate &alculate the vertic vertical al movemen movementt of point % and 6. 6.
TRA8! (!(R<>
Room 206 JPD Building 1955 CM Recto Avenue, Manila Telepone !um"e#$ %02& 516 '559 ()Mail$ mega#evie*+200 -.aoo/com
2
Pδ U
=
W
U
=
2
=
P L
U
AEδ
2
ν = −
=
2L
2AE
;here : @ ' strain energy
nia=ial t#e33$
εx
?ooe3 ;a*$
; ' wor+
PRO!"# / 6or the given truss shown P ' $)) 89, A ' m and B ' ) o/ %ssume that both members of the truss have the same a0ial rigidity %" whose % ' /)) mm* " ' *)) >Pa a. b. c.
εy
ε
=
υ
εx
E
=
υx
εy
E
υy
=
εz
E
=
υ
z
E
Multia=ial t#e33$
6ind the strain energy of the two bars. 6ind the deformation of each bar. 6ind the vertical displacement of =oint .
ε ε ε
PRO!"# ( Three round bars having the same length ! but different shapes are shown. 4isregard the weights of the bars. If d ' *))mm " ' $3) >Pa ! ' ,m P ' ,)89 a. 4etermine the strain energy of the first bar. b. 4etermine the strain energy of the second bar. c. 4etermine the strain energy of the third bar.
x y z
=
1 - ν E - ν
- ν - ν σ x
1
1
- ν σ y
- ν
1
σ z
PRO!"# D % steel rectangular bloc+ 1 in. wide in. deep and in. long is sub=ected to an a0ial tensile load of 10/5 ip3. #easurements show the bloc+ to increase in length by 2/=10) in/ and to decrease in width by 0/21=10) in. a. 4etermine the modulus of elasticity of the material b. 4etermine PoissonEs ratio of the material.
D8;ATAT87! e is the change in volume per unit volume. It is also eual to volumetric strain. e =
∆V
e
=
V
εx
+
εy
+
εz
when a material is sub=ected to a hydrostatic pressure p e ' ) where:
8MPACT ;7AD8!<
p
K
E'
E 3(1
E
2 )
stress e
E is the bul+ modulus of the material or modulus of compression of the material
ea# Modulu3, <
< '
( 21
F&
PRO!"# $) % short solid cast iron cylinder is sub=ected to a0ial and radial compressive stresses 3) #Pa and $) #Pa respectively. 6or " ' $)) >Pa, v G, d ' $*)mm and ! ' *)) mm. a. b. c.
δ
st
δ
=
max
@
MgL
δ max = δ st
AE
=
Mv 2 L AE
2g
1 + 1 +
1
2h
δ st
8mpact acto#
2
δ
max
=
2hδst
δ max δ st
' velocity of the falling mass
PRO!"# 7 % round prismatic steel bar length ! ' *.,m and diameter d ' *) mm hangs vertically from a support at its upper end. % sliding collar of mass # ' *) +g drops from a height h ' $,)mm onto the flange at the lower end of the bar. a. &alculate the ma0imum elongation of the bar due to the impact. b. &alculate the corresponding impact factor. . &alculate the ma0imum tensile stress in the bar.
P787! RAT87 υ ) lateral strain C a0ial strain
4etermine the change in the length and diameter. 4etermine dilatation. 4etermine the change in volume.
PRO!"# $$ % steel bloc+ ,)mm along 0 (,mm along y and $))mm along ? is sub=ected to hydrostatic pressure p ' $,) #Pa. @se " ' *)) >Pa and v ' )., a. b. c.
4etermine the shear modulus. 4etermine the volumetric strain. 4etermine the change in volume.
