-t T i { ti I APPENDIX A UNSOLVED PROBTEMS COMPUTER GRAPHICS l. A line from two points A (10, 30) and B (g0, 70) is to be scaled by factor .1, in X direction and''2' in I/ direction and to be translated by vector (30, 40). Determine the transformation matrix and co-ordinates of transformed line. 2. A triangle having vertices (3, 3), (8, 5), (5, 8) is first translated by 3 units in x-direction then it is scaled by 2 units about fixed point (5, 6) and finally it is rotared about poinr (2, 5) in clockwise direction by 35'. Find the final position of triangle. Show the total transformation on graph paper. FEM l. Consider the bar shown in figure. An axial load P is applied as shown. Determine the elemental stresses and reaction force using FEM. 42-=0.0\t12-m\rn dr: o ll?t C4P\ E= rox loehr/mz 6t*a o 3{8 r-$}q P=100N 4 Sz *o ,&ta* fl( 2. The stepped shaft shown in Figure I is fully restrained against rotation about its axis. Twisting moments of l0 and ti fN-m are applied at the point of changing section. Calculate the rotation of the bar about its axis at point 2 and 3 and hence determine the ;T:":[JH1I: ffi]?l:!ffi:ilJjjf ]:ltrf 3:1'J'3$,;! of ,orque a,ong,he J =2x1o7rro J=3x 1o7mma J=2x 1o7mma 3. Analyze the following stepped bar using FEM i.e. to find nodal displacement, element stresses and reaction forces. 4l = 0 03e\ (,: -5S S trl Ar^: -6\'s r'f {
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APPENDIX AUNSOLVED PROBTEMS
COMPUTER GRAPHICS
l. A line from two points A (10, 30) and B (g0, 70) is to be scaled by factor .1, inX direction and''2' in I/ direction and to be translated by vector (30, 40). Determine thetransformation matrix and co-ordinates of transformed line.
2. A triangle having vertices (3, 3), (8, 5), (5, 8) is first translated by 3 units in x-directionthen it is scaled by 2 units about fixed point (5, 6) and finally it is rotared about poinr(2, 5) in clockwise direction by 35'. Find the final position of triangle. Show the totaltransformation on graph paper.
FEM
l. Consider the bar shown in figure. An axial load P is applied as shown. Determine theelemental stresses and reaction force using FEM.
42-=0.0\t12-m\rn dr: o ll?t C4P\E= rox loehr/mz 6t*a o 3{8 r-$}qP=100N
4 Sz *o ,&ta* fl(2. The stepped shaft shown in Figure I is fully restrained against rotation about its axis.
Twisting moments of l0 and ti fN-m are applied at the point of changing section.Calculate the rotation of the bar about its axis at point 2 and 3 and hence determine the
;T:":[JH1I: ffi]?l:!ffi:ilJjjf ]:ltrf 3:1'J'3$,;! of ,orque a,ong,he
J =2x1o7rro J=3x 1o7mma J=2x 1o7mma
3. Analyze the following stepped bar using FEM i.e. to find nodal displacement, elementstresses and reaction forces.
4l = 0 03e\(,: -5S S trl
Ar^: -6\'s r'f
{
AppendV\\\\
\ \
tt1; =.r4cb,,,,ozEi: = s34bpuPr = 60KN:.
A1 = l2oo rrrm?
Ez = 70 GpaPz=75KN
l:: = 60omm2
E: = 2@Gpa
4.
5.
Modify the above problem by changing the direction of p, & p,For pin jointed truss shown in foilowing fig, determine the nodar'dispracement, stress in
1200 cm
6. The following tig shows a pin-jointedtruss. Cros-sectional area of each elementis 350mm2. E =2@ Gpa. Model thetruss using one_dimensional elements,and determine stress in each element,displacement of joints, and reactions atthe support.
For the truss shown in fig. a horizontal load
:f p_= 4KN is apptied in x directisn u, oJ*,2: Treating Frame as made up of linearelements, determine the global stifiness matrixand reaction force at node 2 in the y_direction.The following fig shows a composite barcarrying force p = 60 KN. 8,".r = 2OC Gpa.EAru* = 70Gpa. Connecting, pjaie ana.*att,
1m
7.
8.Aa400mm'zE=200GPa
are rigid.
Treating each member as one_dimensional linear element.
Alum tube
A = +00 mm2
202
Determine :
Computer Graphics lncluding CAD, AutoCAD and C
(a) Stresses in each member.(b) Displacement-of a load point.(c) Reactions ar wail
OPTIMIZATION
l' A sinrply supported beam is having rectangular cross-section. Distance between support
;"m]he load acting at
""r't* "r beam is 8.5 KN.;;rign beam with fo[owing
finptor of Safety = 1.6Depth/Breadth(k) = 2.5
15mm <d<l50mmSolve for min. deflection.
2' Design a tensile bar for maximum energy absorption for the forowing :
' fi,,ir'rl',"#;TJ,',?:J- is to be designed for minimum torsionar deflection subjected to
Torque applied = g0KN_cmLength '/' shourd lie between 300 mm to 500 mm. Inside diamerer D, > l0 mmOutside diameter Do S 40 mmRatio of outside diameter to inside diameter:
Do
', = I')
Factor of safety = 1.9Following materiars are avairabre : sAE 1020. sAE 1035, sAE 3140. Ar. ailoy no. 39.4. Design a circular shaft for minimum torsional deflection.(i) Length should be berween O6Om and 900 mm.(li) Diameter should be berween l0mm and 70mm(lii) Factor of safety = 1.45
(iv) Twisting moment T = g5 KN_cm.(u) Available materials :
e bar is subjected to a load of 60 KN. It is decided to use a factor of safety of t .5.of the bar is around 550 mm. The bar should have an area > 15 mm2. Designfor,minfrnufr bost, Available materials are SAE 1030, SAE 1095, Aluminium,
6. A cant ver bearn of length 'L' carries a transverse load F = 15 KN at its free end.
Lethe
Detern{e the diameter of beam and length for maximum energy absorption for followingconditiorl. The diameter should be between 30 mm to I00 mm. The length should bebetween &lOrn* to 700 mm. Factor of safety N=1.75. Available mateials are steel
ry, steet SAE 324O. Aluminium alloy no 38. aL= €f m6t
