8-26 to 8–31 For each built-up section shown in Figs. P8–26 to P8–31, determine themoment of inertia and the radius of gyration of the section with respect tethe horizontal centroidal axis.+12 in. X 1 in. plate300 mm X 20 mm plateW14 X 61C250 × 0.438100 mm300 mm X 20 mm plate-12 in. X1 in. plateFIGURE P8-26FIGURE P8-27

Answered: Image /qna-images/answer/596d9f6d-69a3-4a05-b7ce-7585d4898be8.jpg

Answered: nd the radius of gyration of the secti…

Engineering

Mechanical Engineering

nd the radius of gyration of the secti pidal axis.

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 9.87RP

See similar textbooks

Related questions

Q: From the figure shown, if b = 3 units, determine: Inclination of the principal axes, in degrees…

Q: Calculate the moment of inertia of the shaded area about the x-axis. Ix=?

A: To determine the moment of inertia about x-axis.

Q: For the solid area, what is the second moment about the y axis? C. (include units with answer) For…

Q: ab) What is the composite area's moment of inertia based on axis Yo?

A: we have to determine the MOI

Q: Find the polar moment of inertia of the region

A: Given: x2-y2=1x2-y2=9xy=2xy=4To determine:Ploar moment of inertia

Q: Locate the centroid of the cross-sectional área. B. Determine the moments of inertia and the product…

A: As, per the guidelines, I can solve only first three subparts. For rest parts, repost in a separate…

Q: Find the center of mass and moment of inertia respect to x and y for following diagram. a a a

A: Given: The length of the side of an equilateral triangle is a. The triangle can be redrawn as, In…

Q: 2. Find the moment of inertia, radii of gyration and product of inertia considering the figure lies…

A: The moment of inertia of an area with respect to any axis is equal to the centroidal axis plus the…

Q: The moment of inertia with respect to its axis of the solid generated by the revolving an 3V arch of…

A: Write the moment of inertia of the solid generated by the revolving the arc y=sin3x about the…

Q: Calculate the moment of inertia for the the H axis.

A: To find Moment of inertia

Q: What is the moment of inertia about the y-axis of rectangular wooden block with a base of 500mm and…

A: Given Data b=500 mm h=1200 mm

Q: What is the Polar Moment of Inertia?

A: The polar moment of inertia of an area is the second moment of area about an axis perpendicular to…

Q: Moment of Inertia Determine the moment of inertia (ly) for the cross sectional area shown. 2 in. 2…

Q: Suppose that a = 3 in. and b = 7.5 in. Determine the product of inertia for the shaded area with…

A: We have to Determine the product of inertia for the shaded area with respect to the x and y axes.

Q: . Determine the moment of inertia of the

A: To find Moment of inertia of beam's cross-sectional area about the centroidal x and y axes

Q: From the figure shown, if b = 3 units, determine: Moment of inertia about the x-axis, in units4…

Q: Is the moment of inertia for an area different for every axis?

A: The moment of inertia is the resistance or capacity of a core section to resist the bending. The…

Q: Determine the moment of inertia about X-axis and Y-axis

Q: Given the figure below. Find (a) location of the centroid. (b) moments of inertia with respect to…

Q: Find the moment of inertia and radius of gyration about the x-axis using horizontal strips.

A: Given: The equation of parabola: →x=0.510.89y-12-2 The equation of straight line:…

Q: Compute for the moment of inertia about xo and yo of the a) b) 100 mm 75 mm 25 mm 75 mm | = 11 - 12…

A: According to guidelines first will solve in multiple questions given

Q: 3) Find the moment of inertia of a I section (as shown in the diagram) about its CG. 10

A: Please follow the attached detailed solution:

Q: Determine the following based on the given illustration: d) The Radii of Gyration about the X and Y…

Q: What is the moment of inertia with respect to the xy direction (Ixy) ?

A: Given object is divided into 2 parts. To find centroid (C) position: Part Area (cm2) x y Ax Ay…

Q: Find the both moments of inertia (Ix, Iy) by integration around the central coordinates as shown in…

Q: What is the polar moment of inertia of the shaft’s cross-sectional area?

A: Polar moment of inertia: The polar moment of inertia is defined as the sum of polar moment of…

Q: Find the moment of inertia with respect to y-axis the area bounded by * a?y = x3, the y-axis, and…

Q: Determine the moment of inertia of the area shown in Fig. 10-8a about the x axis. - 100 mm - 25 mm…

Q: H 2.2 2,1 A Өк 40° х

Q: Determine the moment of inertia with respect to y-axis?

Q: Find the both moments of inertia (Ix, ly) by integration around the central coordinates hown in next…

Q: Calculate the polar moment of inertia of the shape -3 in.--3 in.- 6 in. 4 in. 2 in.

Q: Using the figure shown below, determine the following: A. Polar moment of inertia B. Polar radius…

A: Draw the schematic diagram of the section. Here, section 1 is a complete rectangle, section 2 is a…

Q: Question # 4. For the shaded area shown in the figure: 100 mm a) Calculate the moment of inertia…

A: y =x2/50 x =50y IX' = ∫y2dA take a small area element dA at a distance y from x-axis dA =2xdy dA…

Q: ) Find the moment of inertia of the cross section to the right about the x and y axes shown. In…

Q: Determine the radii of gyration for the circular with respect to area shown in Fig. The x- and…

A: Given data R=4 inRX=6 inRy=5 in

Q: Determine the moment of inertia of the shaded region about the x and y axis using parallel axis…

A: This is the question of moment of inertia of plane figure. The figure is consists of three different…

Q: Find the moment of inertia about the x-axis of the semicircular

Q: Find the moment of inertia about y-axis

Q: Define the term polar moment of inertia?

A: The Polar Moment of Inertia is a measure of the ability of an object to oppose or resist torsion…

Q: Moment of Inertia rmine the second mor (a) x-axis (b) y-axis

Q: 4. moment of inertia with respect to y-axis (ly) 5. Polar moment of Inertia 6. Radius of gyration…

Q: Figure Q10 shows the shaded area with the equation given. Calculate: y - y² = 1 – 0.5x 1 m 1 m -2 m

A: Given y2=1-0.5x Here moment of inertia represents the distribution of points about the given axis

Q: w. Calculate the moment of inertia about axis z of th

A: GIVEN : Breadth (b)=2cm Height (h)=5cm TO FIND Moment of inertia about Z axis

Q: build the Mohr circles of the axes that pass through the origin and the centroid, showing the…

A: Given data: The height of the outer rectangle is, h=6a. The length of the outer rectangle is,…

Q: centroidal moment of Inertia

Q: Solve for the maximum and minimum moment of inertia. 300mm 300mm 400mm 200mm

Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.

Question

8-26 to 8–31 For each built-up section shown in Figs. P8–26 to P8–31, determine the
moment of inertia and the radius of gyration of the section with respect te
the horizontal centroidal axis.
+12 in. X 1 in. plate
300 mm X 20 mm plate
W14 X 61
C250 × 0.438
100 mm
300 mm X 20 mm plate
-12 in. X1 in. plate
FIGURE P8-26
FIGURE P8-27

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

8-3 Refer to Fig. P8–3. Determine the moment of inertia I and the radius of gyration r, of the circular area about the x axis. 5 in. 10 in. FIGURE P8–3
on 1 Qu ered Semi Circle ed out of ag question Mod 12 Finis a = 200mm, b 400mm, c 400mm For the given composite geometry estimate the moment of inertia about centroidal axis parallel and prependicular to AB. The location of the centroid with respect to point-A: Along x-direction is: mm. (answer to the nearest whole number) Along y-direction is: mm. (answer to the nearest whole number) The moment of inertia with respect to the centroid axis: Parallel to line AB is: mm^4 Perpendicular to line AB is mm^4
8-32 See Fig. P8–32. Determine the radius of gyration of the built-up section shown with respect to the horizontal centroidal axis. The dashed line at the bottom of the section represents lacings for connecting the component parts at the open side. The areas of the lacings are not considered as effec- tive areas when calculating the moment of inertia. -16 in. X 1 in. plate -9.2 in. -C15 × 33.9 \Lacings FIGURE P8–32 8-33 In Problem 8–32, determine the radius of gyration of the built-up section shown with respect to the vertical centroidal axis.
The shaded area shown in (Figure 1) is bounded by x, y axes and the curve y? = 3.24 –- 0.5x m2 , where x is in m. Suppose that a = 6.48 m and h = 1.8 m. Part A Determine the moment of inertia for the shaded area about the x axis. Express your answer to three significant figures and include the appropriate units. µA Iz = Value Units Figure 1 of 1 Submit Request Answer Provide Feedback
8-6 Refer to Fig. P8–6. If the moment of inertia I, of the rectangular area about the x axis is 7320 in.4, determine I, of the area about the 10 in. x' axis. 12 in. 3 in.
T A C -P -m n b
The structural steel column is fixed at its base and free at its upper end. Assume L = 13.0 ft, a = 0.99 in., b = 7.5 in., c = 9.48 in., d = 9.48 in., and t = 0.79 in. At the top of the column, a load P is applied to the stiffened seat support at an eccentricity of e from the centroidal axis of the wide-flange shape. Using the allowable stress method, determine the maximum allowable eccentricity e if (a) P - 18 kips and (b) P = 32 kips. Apply the AISC equations given in Section 16.5 and assume that E = 29,000 ksi and oy = 50 ksi. eccentricity e P y d Cross section
A channel and a plate are welded together as shown to form a section that is symmetrical with respect to the y axis. Determine the moments of inertia of the combined section with respect to its centroidal x and yaxes if a = 14 in. 0.5 in. y C a CS×115 The moment of inertia with respect to the x axis is The moment of inertia with respect to the yaxis is in4 in4 K
The structural steel column is fixed at its base and free at its upper end. Assume L = 13.0 ft, a = 0.99 in., b = 7.5 in., c = 9.48 in., d = 9.48 in., and t = 0.79 in. At the top of the column, a load P is applied to the stiffened seat support at an eccentricity of e from the centroidal axis of the wide-flange shape. Using the allowable stress method, determine the maximum allowable eccentricity e if (a) P = 18 kips and (b) P = 32 kips. Apply the AISC equations given in Section 16.5 and assume that E = 29,000 ksi and oy = 50 ksi. eccentricity e b P y - Cross section
See Fig. P8-7. Determine the polar moment of inertia of the 18-in.-diameter circular area shown 8-7 with respect to pole A on its circumference. D = 18 in. A FIGURE P8–7
Determine the moment of inertia (in mm4) of the given figure with respect to x axis. Assume y=98 mm and z=49 mm. Round off only on the final answer expressed in whole number.
h b Part A Locate the centroid y of the composite area. Set a = 170 mm, b=370 mm, d= 60 mm, h = 250 mm (Figure 1) Express your answer with the appropriate units. y = Submit Part B Value μÅ Request Answer Submit Determine the moment of inertia of this area about the r' axis. Express your answer with the appropriate units. HA L₂= Value Units Request Answer B ? Units ?