3) The T shaped cross-section of a beam is made of a flange (the upper horizontal area A1 = 2000 mm2) and a web (the lower vertical area A2 = 3200 mm?) as shown in the figure. 20 mm a. If you want to compute the vertical distance C, of the centroid of this cross-section from the bottom most point of this cross- section then give the expression in terms of some numbers from which Cy can be computed. No need to carry out the calculation. b. From part (a) if you get Cy = 114.6 mm then give the final expression of the area moment of inertia Ix (about the x-axis going through the centroid of the T-section). Your expression should 160 mm only contain some numbers. No need to finish the calculation. c. Give the final expression of the area moment of inertia ly (about the y-axis going through the centroid). Your expression should 20 mm only contain some numbers. No need to finish the calculation. 100 mm d. If you drill a circular hole of 15 mm diameter with its center coinciding with the centroid point C of the T cross section then should the centroid of the T-section with hole moves (i) up, (ii) down or (iii) remains same relative to the centroid of T-section without hole? [Hint: For a rectangular cross section the area moment of inertia (Ix) about the horizontal axis going through its centroid is given by Ix = bh3/12, where b is width in horizontal direction and h is height]
3) The T shaped cross-section of a beam is made of a flange (the upper horizontal area A1 = 2000 mm2) and a web (the lower vertical area A2 = 3200 mm?) as shown in the figure. 20 mm a. If you want to compute the vertical distance C, of the centroid of this cross-section from the bottom most point of this cross- section then give the expression in terms of some numbers from which Cy can be computed. No need to carry out the calculation. b. From part (a) if you get Cy = 114.6 mm then give the final expression of the area moment of inertia Ix (about the x-axis going through the centroid of the T-section). Your expression should 160 mm only contain some numbers. No need to finish the calculation. c. Give the final expression of the area moment of inertia ly (about the y-axis going through the centroid). Your expression should 20 mm only contain some numbers. No need to finish the calculation. 100 mm d. If you drill a circular hole of 15 mm diameter with its center coinciding with the centroid point C of the T cross section then should the centroid of the T-section with hole moves (i) up, (ii) down or (iii) remains same relative to the centroid of T-section without hole? [Hint: For a rectangular cross section the area moment of inertia (Ix) about the horizontal axis going through its centroid is given by Ix = bh3/12, where b is width in horizontal direction and h is height]
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
![3) The T shaped cross-section of a beam is made of a flange (the upper
horizontal area A1 = 2000 mm2) and a web (the lower vertical area A2 =
3200 mm?) as shown in the figure.
20 mm
If you want to compute the vertical distance C, of the centroid of
this cross-section from the bottom most point of this cross-
а.
section then give the expression in terms of some numbers from
which Cy can be computed. No need to carry out the calculation.
b. From part (a) if you get Cy = 114.6 mm then give the final
expression of the area moment of inertia Ix (about the x-axis going
through the centroid of the T-section). Your expression should
only contain some numbers. No need to finish the calculation.
Give the final expression of the area moment of inertia ly (about
the y-axis going through the centroid). Your expression should
only contain some numbers. No need to finish the calculation.
d. If you drill a circular hole of 15 mm diameter with its center
160 mm
С.
20 mm
100 mm
coinciding with the centroid point C of the T cross section then should the centroid of the T-section with
hole moves (i) up, (ii) down or (iii) remains same relative to the centroid of T-section without hole?
[Hint: For a rectangular cross section the area moment of inertia (Ix) about the horizontal axis going
through its centroid is given by Ix = bh³/12, where b is width in horizontal direction and h is height]
(a)
Cy =
%3D
(d) 1
(b)
Ix =
(c)
ly =
3
%3D
Up
Down
Remains
same](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb418520d-b5b5-42f9-a913-91b3e60591cf%2F97eab623-8192-4d7a-a041-5ef24ca70759%2Ff9xqv8r_processed.png&w=3840&q=75)
Transcribed Image Text:3) The T shaped cross-section of a beam is made of a flange (the upper
horizontal area A1 = 2000 mm2) and a web (the lower vertical area A2 =
3200 mm?) as shown in the figure.
20 mm
If you want to compute the vertical distance C, of the centroid of
this cross-section from the bottom most point of this cross-
а.
section then give the expression in terms of some numbers from
which Cy can be computed. No need to carry out the calculation.
b. From part (a) if you get Cy = 114.6 mm then give the final
expression of the area moment of inertia Ix (about the x-axis going
through the centroid of the T-section). Your expression should
only contain some numbers. No need to finish the calculation.
Give the final expression of the area moment of inertia ly (about
the y-axis going through the centroid). Your expression should
only contain some numbers. No need to finish the calculation.
d. If you drill a circular hole of 15 mm diameter with its center
160 mm
С.
20 mm
100 mm
coinciding with the centroid point C of the T cross section then should the centroid of the T-section with
hole moves (i) up, (ii) down or (iii) remains same relative to the centroid of T-section without hole?
[Hint: For a rectangular cross section the area moment of inertia (Ix) about the horizontal axis going
through its centroid is given by Ix = bh³/12, where b is width in horizontal direction and h is height]
(a)
Cy =
%3D
(d) 1
(b)
Ix =
(c)
ly =
3
%3D
Up
Down
Remains
same
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