Namas Chandra Introduction to Mechanical engineering Hibbler Chapter 2-1 EML 3004C Problem 6-5 (page 256) Determine the location (x’,y’) of the centroid of the shaded area. Solutio n: Area of the differential element dA = ydx = (1/x)dx and xc xc A xc d A 1 d xc 0.5 2 x x 1 x d 0.5 2 x 1 x d xc 1.08in yc A yc d A 1 d yc 0.5 2 x 1 2x 1 x d 0.5 2 x 1 x d in yc 0.541 in
Problem 6-5 (page 256)
Feb 22, 2016
Problem 6-5 (page 256). Determine the location (x’,y’) of the centroid of the shaded area. . Solution:. Problem 6-20 (page 259). Determine the distance y’ to the center of gravity of the volume. The material is homogeneous. Solution:. Problem 6-25 (page 263). - PowerPoint PPT Presentation
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Namas ChandraIntroduction to Mechanical engineering
HibblerChapter 2-1
EML 3004C
Problem 6-5 (page 256)
Determine the location (x’,y’) of the centroid of the shaded area.
Solution:Area of the differential element dA = ydx = (1/x)dx and xc = x, yc= y/2 = 1/(2x)
xc
Axc
d
A1
d
xc0.5
2
xx1x
d
0.5
2
x1x
d
xc 1.08in
yc
Ayc
d
A1
d
yc0.5
2
x12x
1x
d
0.5
2
x1x
d
in yc 0.541in
Namas ChandraIntroduction to Mechanical engineering
HibblerChapter 2-2
EML 3004C
Problem 6-20 (page 259)
Determine the distance y’ to the center of gravity of the volume. The material is homogeneous.
Solution:
The volume of the differential thin disk element dV = y^2dz = (a^2-z^2)dz and zc = z
zc
Vz
d
V1
d
zc0
a
zz a2 z2
d
0
a
z a2 z2
d
zc38
a
Namas ChandraIntroduction to Mechanical engineering
HibblerChapter 2-3
EML 3004C
Problem 6-25 (page 263)
Determine the location (x’,y’) of the centroid of the area.
Solution:
yc
yc A
A yc
1 4 2( )[ ] 4 8 2( )[ ] 7 4 2( )[ ]2 4( ) 2( ) 8 2( )
in yc 4 in
xc
xc A
A xc
1 8 2( )[ ] 4 2 4( ) 2( )[ ]2 4( ) 2( ) 8 2( )
in xc 2.5in
Namas ChandraIntroduction to Mechanical engineering
HibblerChapter 2-4
EML 3004C
Problem 6-35 (page 265)
Determine the distance x’ to the center of gravity of the generator assembly. The weight and the center of gravity of each of the various components are indicated below. What are the vertical relations at blocks A and B needed to support the assembly?
Solution:W 200 1000 250 W 1450lb
xc W MA 1450xc 200 1( ) 10004( ) 250 8( )
xc 4.276ftEquilibrium :
Namas ChandraIntroduction to Mechanical engineering
HibblerChapter 2-5
EML 3004C
Problem 6-35 (continued)
xc 4.276ftEquilibrium :
MA 0 By 10( ) 14504.276( ) 0 By 620 lb
Fy 0 Ay 620 1450 0 Ay 830 lb
Namas ChandraIntroduction to Mechanical engineering
HibblerChapter 2-6
EML 3004C
Problem 6-76 (page 289)
Determine the moment of inertia of the shaded area about the x axis.
Solution:
Area of the differential element (shaded) dA = 2x dy where x = a/b(b^2-y^2)^1/2, hencedA = 2x dy = 2a/b(b^2-y^2)^1/2 dy
Ix Ax2
d Ix
2
2
xx2 114
x2
d Ix
2
2
xx2 14
x4
d
Ixb3
4
Namas ChandraIntroduction to Mechanical engineering
HibblerChapter 2-7
EML 3004C
Problem 6-82 (page 293)
The composite beam consists of a wide-flange beam and cover plates welded together as shown. Determine the moment of inertia of the cross-sectional area with respect to a horizontal axis passing through the beam’s centroid.
Solution:
Ixcxc112
175( ) 200( )3 112
160 1703 2112
275153 2 15 275 107.52
mm4
Ixcxc 1.467 108 mm4
Namas ChandraIntroduction to Mechanical engineering
HibblerChapter 2-8
EML 3004C
Problem 6-95 (page 295)
Determine the distance y’ to the centroid of the plate area.
Solution:
Area of the differential element dA = y dx = (1 - 1/4(x^2)) dx and yc = y/2 = 1/2(1-(1/4)x^2)
yc
Ayc
d
A1
d
yc2
2
x12
114
x2
114
x2
d
2
2
x114
x2
d
m yc 0.4m
Related Documents
