ermine the location of the centroid for the cross-section shown below an cch of the cross-section, clearly showing the centroid and indicate its di= cted origin. (Start your calculations be setting an origin at the bottom, he cross-section). culate the second moments of areas about the centroidal axes for th ion. 100 mm y 10 mm

ermine the location of the centroid for the cross-section shown below an cch of the cross-section, clearly showing the centroid and indicate its di= cted origin. (Start your calculations be setting an origin at the bottom, he cross-section). culate the second moments of areas about the centroidal axes for th ion. 100 mm y 10 mm

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.13P: Figure (a) shows the cross section of a column that uses a structural shape known as W867...

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Figure (a) shows the cross section of a column that uses a structural shape known as W867 (wide-flange beam, nominally 8 in. deep, weighing 67 lb/ft). The American Institute of Steel Construction Structural Steel Handbook lists the following cross-sectional properties: A=19.7in.2,Ix=272in.4, and Iy=88.6in.4. Determine the dimensions of the rectangle in Fig. (b) that has the same Ix and Iy as a W867 section.
Figure (a) shows the cross-sectional dimensions for the structural steel section known as C1020 (channel with a nominal depth of 10 in., weighing 201b/ft). The American Institute of Steel Construction Structural Steel Handbook lists the following properties for the cross section: A=5.88in.2,Ix=78.9in.4, and Iy=2.81in.4. If two of these channels are welded together as shown in Fig. (b), find Ix and Iy for the resulting cross section.
Determine the locationof the centroid for the cross-section shown below and draw a scaled sketch of the cross-section, clearly showing the centroid and indicate its distance from the selected origin. (Start your calculations be setting an origin from the bottom, left-most point on the cross-section). 2 Calculate the second moments of areas about the centroidal axes for the beam cross- section. 60 mm |10 mm 10 mm 100 mm 10 mm 40 mm
3.1 Determine the location of the centroid for the cross-section shown below and draw a scaled sketch of the cross-section, clearly showing the centroid and indicate its distance from the selected origin. (Start your calculations be setting an origin from the bottom, left-most point on the cross-section). 3.2 Calculate the second moments of areas about the centroidal axes for the beam cross- section. 60 mm 10 mm y 10 mm 100 mm 10 mm 40 mm
Determine the location of the centroid for the cross-section shown below and draw a scaled sketch of the cross-section, clearly showing the centroid and indicate its distance from the selected origin. (Start your calculations be setting an origin at the bottom, left-most point on the cross-section). Calculate the second moments of areas about the centroidal axes for the beam cross- section. 100 mm y 10 mm 10 mm 10 mm Figure 3: Cross-section 150mm 100 mm
3.1 Determine the location of the centroid for the cross-section shown below and draw a scaled sketch of the cross-section, clearly showing the centroid and indicate its distance from the selected origin. (Start your calculations be setting an origin at the bottom, left-most point on the cross-section). 3.2 Calculate the second moments of areas about the centroidal axes for the beam cross- section. 100 mm y z 10 mm 10 mm 10 mm Figure 3: Cross-section ww OSt 100 mm
3.1 Determine the location of the centroid for the cross-section shown below and draw a scaled sketch of the cross-section, clearly showing the centroid and indicate its distance from the selected origin. (Start your calculations be setting an origin at the bottom, left-most point on the cross-section). 3.2 Calculate the second moments of areas about the centroidal axes for the beam cross- section. 100 mm у z X 10 mm 10 mm 10 mm Figure 3: Cross-section ww 00L ww OSL
3.1)Determine the location of the centroid for the cross section shown in Figure 3 and draw a scaled sketch of the cross-section, clearly showing the centroid and indicate it's distance from the selected origin. (Start your calculations be setting an origin at the bottom, left most point on the cross section). 3,2)Calculate the second moment of areas about the centroidal axes for the beam cross-section from Figure 3.
The cross sectional dimensions of a beam are shown. If the flange thickness, h, is 12.5 mm, determine the vertical distance from the bottom edge of the flange to the centroid of the cross section. Note: State your answer in mm Note: Do NOT include units in your answer. Answer: ISO HH (20 m
For the area below, evaluate 1. The (x,y) coordinates of the centroid (please mark your origin or reference point on the diagram) 2. The 2nd moments and product of area in centroidal-based xy (horizontal-vertical) coordinates 3. The principal 2nd moments of area, and the direction of the first principal axis relative to the horizontal (x) axis (anticlockwise positive) 50 75 30 150 60 50 15 Figure 1: Cross section (all dimensions in mm) Quantity Xc (please mark your origin on the diagram) Yc (please mark your origin on the diagram) Ix ly Ixv I₁ I₂ a1 (please show the direction) Value 30 Units
Compute the coordinates of the centroid (, y) of the area shown. Also compute the area moment of intertia about the x and y axes shown in the figure and the x' and y' axes with origin at the centroid. y y = a/bx BY NC SA 2016 Eric Davishahl Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value а 2.5 in 1.1 in1 (Note the -1 exponent only applies to the unit, not the number.) 8 in The x coordinate of the centroid is a = in. The y coordinate of the centroid is j in. The moment of inertia about the x axis is 1, in“. The moment of inertia about the y axis is Iy in“. The moment of inertia about the x' axis going through the centroid is I' in“. The moment of inertia about the y' axis going through the centroid is Iy in“.
Question 3 3.1 Determine the location of the centroid for the cross-section shown belowand drawa scaled sketch of the cross-section, clearly showing the centroid and indicate its distance from the selected origin. (Start your calculations be setting an origin from the bottom, left-most point on the cross-section). 3.2 Calculate the second moments of areas about the centroidal axes for the beam cross- section. 60 mm 10 mm y x 10 mm 100 mm 10 mm 40 mm