teme gd i civil engineering

8/12/2019 Teme Gd i Civil Engineering

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FACULTY OF CONSTRUCTIONSDep.: CIVIL ENGINEERING

HOMEWORKS

Homework no. 1: Gr p!"# $ Con%&r'#&"on%

Homework no. (: T!e )o"n&

1. Represent in orthographic representation on two planes of projection, the

folowing points: A(70,20,40); B( ,!20,4 ); "(4 ,10,!#0); $(10,0,# ); %(1 ,0,0); &(' ,40,0); (!40,20!2 ); (! 0,!# ,!10); *(2 ,!#0,! 0).

Obs. : +pecif the space position of the points (the -ihe-ral angles).

2. Represent in orthographic representation on three planes of projection, thefolowing points:

A(40,1 ,10); B(!#0,20, ); "(!10,!2 ,!2 ); $(20, ,!#0).

Obs. : +pecif the space position of the points (the trihe-ral angles).

#. Represent the projections of the triangle AB", on three planes of projection,nowing that the /erte A lies on the isecting plane B , the /erte B issit ate- in the 3 a-rant an- the /erte " elongs to the hori ontal plane56 .

Obs. : +pecif the coor-inates of the points.

4. 8ne gi/es the point 9(10,#0,20). 8ne re3 ires to represent on three planes ofprojection the folowing points:

! the point 9;! the s etrical 9 1 of the point 9 si-e 56 ;! the s etrical 9 2 of the point 9 si-e 5 ;! the s etrical 9 # of the point 9 si-e 5< .


2/13

Homework no. *: T!e %&r "+!& $"ne

1. 8ne gi/es the line ($) -efine- the points A an- B. 8ne re3 ires to fin-:

- =he traces of the line: 6(h,h>,h?), (/,/>,/?) an- ,w?);- =he regiones passe- the line.

A(1 , ,' ); B(@0, 0,10).

2. 8ne gi/es the straight line ($) -efine- the points A an- B, respecti/ethe point 9( , >) not l ing on that line. 8ne re3 ires to constr ct thro ghthe point 9( , >), a hori ontal line ( ) an- a frontal line (&) intersectingwith ($). 8ne wor s on three projections.9(10,40,10); A(!#0,20,10) an- B(2 , ,40).

#. 8ne gi/es the straight line ($) -efine- the points A an- B, respecti/e

the point 9( , >) not l ing on that line. 8ne re3 ires to constr ct thro ghthe point 9( , >), a line ( 1) parallel to ($) an- a line ( 2) non intersectingwith ($).9(2 ,20,20); A( 0,#0,1 ) an- B(1 , 0,40).

4. Represent in three projections all the t pes of partic lar seg ent!linesha/ing the tr e length #0 .

. $eter ine the tr e length of the seg ent line (AB) an- the angles an-C etween the line an- the projection planes.

A( 0,10,2 ); B(20,20,10).


3/13

Homework no. ,: THE )LANE

1. 8ne gi/es three points (not l ing on a line): A(40,14,2 ); B(2@,',40);"(4 ,',# ). 8ne re3 ires to -eter ine the traces )-)- )/ of the plane-efine- the pre/io s points an- the a i angle 0 etween theplane 5 ) an- the hori ontal projection plane H2.

2. $eter ine the line of intersection etween two opa3 e plates: the plate

A3C2 sit ate- in a hori ontal plane (or H2 parallel) ha/ing thecoor-inate D4 , respecti/el the o li3 e (s ew) plate MN)2 . +t -also, the /isi ilit of the plates.

A(10#, @0, 4 ); B( , 10, 4 ); "(1 , 100, 4 );9(110, 20, #0); E('0, 10 , F0); G(1 , 0, 10).

#. $eter ine the intersection (piercing) point etween the straight lineD45-567 -efine- the points M an- N an- the triang lar plate 5 A3C .+t - the /isi ilit of the line after the intersection.

A(1 , 1 , # ); B( 0, , '0); "(@ , 2 , 10);9(1@, 47, 1 ); E(70, 1 , 4@).

4. $eter ine the line of intersection etween the plates 5 A3CD an- )8R2-sing a iliar projecting planes. +t - also the /isi ilit of the plates.

A(F0, 10, 10); B(2 , , ); "( , 40, ); $( , 4 , );G(@0, , 40); E(#0, , 0); "( , 10, ' );

Eot : All the plates are opa3 e .


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Homework no. 9: THE METHODS OF D.G. T!e %';%&"&'&"on oe$pomen&%.

1. Represent a c e (he ahe-ron) with the si-e # , ha/ing a facecontaine- in a /ertical projecting plane 5 R : R ('0, 0, 0), the angleOR R J4 .

2. 8ne gi/es a right p ra i- ha/ing as ase a reg lar pentagon inscri e- ina circle with the ra-i s rJ2 , sit ate- in the plane 5 H . =he altit -e ofthe p ra i- is 7 . 8ne re3 ires the tr e si e of the plane section inp ra i- with a /ertical projecting plane 5 8 an- the -e/elop ent of thep ra i- fr st etween the c tting plane an- the ase. I O8 8 J#0M.

#. 8ne gi/es the o li3 e p ra i- A3CD@ : A(@0,2 , 0); B('0,4 , 0); "(40,20,0); $(7 , 7, 0); (1 , 0, 0). 8ne re3 ires the tr e si e of the plane sectionin p ra i- with a /ertical projecting plane 5 ) an- the -e/elop ent of thetr ncate- p ra i- etween the c tting plane an- the ase. G (2 , 0, 0);I8G G>J1# M.

4. 8ne gi/es the frontal pris A3CDA 13 1C 1D1. 8ne re3 ires to -eter inethe plane section with a plane 5 ) perpen-ic lar to the pris e-ges an-the -e/elop ent of the pris portion etween the c tting plane an- thease.

A(@ , 7,0); B( 101,2', 0); "(7@,4', 0); $('',##, 0); A 1(7, 7,'');G (1#, 0, 0).


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Homework no.J: )OLYHEDRONS. )$ ne %e#&"on% n55e>e$pomen&%. T!e "n&er%e#&"on w"&! %&r "+!& $"ne.

1. $eter ine the plane section with the o li3 e plane 5 ) in the p ra i- A3CSan- the -e/elop ent of the p ra i- fr st etween the c tting plane an-

the ase.

A(@#, 1, 0); B('7, 21, 0); "( 40, #0, 0); +( 2#, 7 , '#);G (1#, 0, 0); I8G GJ122N; I8G G>J140N.

2. 8ne gi/es the 3 a-rilateral right pris with the ase A3CD containe- in 5 H ,ha/ing the altit -e ' . 8ne re3 ires to fin- the plane section with theo li3 e plane 5 ) in pris , the tr e si e of the section an- the -e/elop ent ofthe pris portion etween the c tting plane an- the pper ase (incl si/elthe ases).

A(@ , 2@, 0); B( 0, 0, 0); "(#', #0, 0); $(' , , 0);G (10, 0, 0); I 8GJ'0M; I 8G>J#0M.

#. 8ne gi/es the o li3 e p ra i- SA3C with the ase A3C containe- in theplane 5 H : A(12 ,4 ,0); B('2,@0,0); "(F0,@,0); +(7,40,7 ). $eter ine thepoints of intersection (piercing points) etween the p ra i- an- the seg entline ( MN). +t - also, the /isi ilit of the line.

9(10 ,70, ); E(#4,20, ).

4. 8ne gi/es the triang lar o li3 e pris A3CMN) with the ase A3C l ing in5H . $eter ine the plane section in pris with the o li3 e (s ew) plane 5 ) ,the tr e si e of the section an- the -e/elop ent of the pris portion etweenthe c tting plane an- the lower ase (incl si/el the ases).

A(1 , 10, 0); B( 20,#0, 0); "(40,1 , 0); 9(' ,40, 0);G (@0, 0, 0); I8G GJ4 M; I8G G>J4 M.


10/13

Homework no. 1 : THE CONE AND THE CYLINDER.

1. 8ne consi-ers a cone of re/ol tion ha/ing the ase a circle with ra-i sRJ#0 , containe- in the plane 5 @, the /erte S4%-% 7an- the altit -e 70 (as perpen-ic lar line to 5 ). $eter ine the tr e si e of an elliptical

section c tting the cone with a hori ontal projecting plane 5 8 an- the-e/elop ent of the cone fr st etween the c tting plane an- the ase(incl si/el the ases).

2. 8ne gi/es a cone of re/ol tion ha/ing the ase a circle with ra-i s RJ#0, containe- in the plane 56 , the /erte (/,/>) an- the altit -e 70 .

" tting the cone with a /ertical projecting plane 5 ) , one re3 ires the tr esi e of a para olical section in cone an- the -e/elop ent of the tr ncate-cone etween the plane 5 ) an- the ase (incl si/el the ases).

#. $eter ine the tr e si e of a plane section with a /ertical projecting plane

5) in the c lin-er of re/ol tion, ha/ing the ase a circle with ra-i s RJ#0, containe- in the plane 56 , an- the altit -e 7 . Represent also

the -e/elop ent of the tr ncate- c lin-er etween the plane 5 ) an- thease (incl si/el the ases).

4. 8ne gi/es the right c lin-er ha/ing the ase a circle l ing in 56 with thecentre (@ ,#0,0), the ra-i s RJ2 an- the altit -e 70 . 8nere3 ires to fin- the plane section with the o li3 e plane 5 ) , the tr e si eof the section an- the -e/elop ent of the c lin-er portion etween thec tting plane an- the lower ase (incl si/el the ases).

G (0, 0, 0); I8G GJ1# M; I8G G>J1 0M.

5. 8ne consi-ers the o li3 e plane, ha/ing the -irectri a circle l ing in 56 ,with ra-i s rJ20 , the centre (40,#0,0) an- the /erte +(0, 0, 0).8ne re3 ires the tr e si e of a section with the /ertical plane 5K(hori ontal projecting plane) gi/en its traces an- the -e/elop ent ofthe lateral s rface of the cone.

K (!1 ,0,0); I8G GJ 0M.


11/13

Homework no. 11: )RO ECTIONS WITH [email protected]$>"n+ &!e roo


12/13

Homework no. 1(: )RO ECTIONS WITH [email protected]$>"n+ &!e p$ &


13/13

2. $eter ine the o n-ar lines of the e an ents for a hori ontalplatfor an- for the acces roa- of the constr ction site gi/en itsconto r lines. =he slopes of the e an ents are:

! for the c t J 1P1

! for the fill J 2P#! the slope of the acces roa- is : 1P7=he -rawing scale is 1:200.

R J 7 . 0 : D 0.00

0

4F

4@

47

0 1 2 # 4

4 F

4 @

4 7

4 '

4

4 4

'[email protected]. 0

21. 0

teme gd i civil engineering

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