Tutorial 5 Properties of Lines, Areas and Volume
EME1016 Applied Statics Tri.1_2018/2019
Tutorial-5 (Properties of Lines, Areas and Volume)
(1) Locate the centroid ( x, y ) of the shaded area shown below:
Ans. :A( x, y =1.13m, 3.6m)
Ans. : B( x, y = (5a)/8, (2ka)/5)
Ans. : C( x, y = 3b/4, 3h/10)
Ans. : D( x, y =4a/3 , 4b/3 )
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Tutorial 5 Properties of Lines, Areas and Volume
(2)
EME1016 Applied Statics Tri.1_2018/2019
For the uniform wires bent in the figures shown below, Locate:
(a)- the centroid ( x & y ), of Fig.A
(b)- the centroid ( x , y , z ), of Fig.B
Ans.: A ( x, y =24.4mm , 40.6mm)
(3)
Ans. :B( x , y , z = 0.074m,, 0.037m,, 0 .157m)
For the member’s cross-sectional areas shown below; Locate:
(a)- the centroid ( x
& y ), of the cross-sectional area, Fig.A,
(b)- the centroid ( x
& y ), of the angle’s cross-sectional area, Fig.B.
Ans.: A ( x, y = 2.73m, 1.42m)
Ans.: B ( x, y =77.2mm, 31.7mm)
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Tutorial 5 Properties of Lines, Areas and Volume
(4)
EME1016 Applied Statics Tri.1_2018/2019
For the beam’s cross-sectional areas shown below;
(a)- Determine the distance ( y ), the centroid then Find the moment of inertia (Īx`) about the
x` - axis,
(b)- Determine the moment of inertia ( I x & I y ) about the x & y -axes.
Ans. :( y =170.0mm, and Īx`, Īx , Īy=722(106) mm4, 2.17(103) mm4, 91.7(106) mm4)
(5)
Determine the volume and the total surface of the body shown below;
Ans.: (V = 255x103mm3)
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Tutorial 5 Properties of Lines, Areas and Volume
(6)
EME1016 Applied Statics Tri.1_2018/2019
Locate centroid y of the paraboloid.
Ans. :( y =2.67m)
(7)
For the cross-sectional area of the T-beam,
(a)Determine y , which locates the centroidal axis x` for the cross-sectional area of the Tbeam,
(b) Find the moments of inertia Īx` about x` - axis.
Ans. : ( y =48.25mm and Īx` =15.1x106mm4)
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Tutorial 5 Properties of Lines, Areas and Volume
(8)
EME1016 Applied Statics Tri.1_2018/2019
The king’s chamber of the Great Pyramid of Giza is located at its centroid. Assuming the
pyramid to be a solid, prove that this point is at Z = ¼ h, suggestion: Use a rectangular
differential plate element having a thickness dz and area (2x)(2y).
Ans. :( Z =h/4)
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Tutorial 5 Properties of Lines, Areas and Volume
(9)
EME1016 Applied Statics Tri.1_2018/2019
Determine the moments of inertia, Īx and Īy of the beam’s cross-sectional area about x and
y- axis.
Ans. : (Īx = 115X106 mm4; Īy =153X106 mm4)
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