### Moment of Inertia Calculation for Composite Section#### Diagram Description:The diagram represents a composite section consisting of a wide flange beam (W shape) placed over a C-shaped channel.1. **Wide Flange Beam:** - Designation: W 8x40 - The section is shaped like the letter "H", representing a standard wide-flange beam.2. **C-Shaped Channel:** - Designation: C 8x13.75 - The C-shaped channel is positioned below the wide flange beam, with its open side facing downward. #### Labels:- Two important dimensions are labeled: - **bf**: This likely represents the width of the flange. - **t**: This likely represents the thickness of the web of the section. #### Task:- The task specified is to find \(I_x\), which is the moment of inertia about the x-axis for the composite section.### Detailed Explanation:To calculate the moment of inertia \(I_x\) for the composite section, follow these steps:1. **Break Down the Section:** - Separate the wide flange beam (W 8x40) and the C-shaped channel (C 8x13.75).2. **Determine Individual Moments of Inertia:** - Calculate the moment of inertia for the wide flange beam and the C-shaped channel individually, using standard formulas for these shapes.3. **Use Parallel Axis Theorem:** - For any component that is not centered on the x-axis, use the parallel axis theorem to find its moment of inertia relative to the x-axis of the composite section. \[ I_{x'} = I_x + Ad^2 \] where: - \(I_{x'}\) is the moment of inertia about the composite centroidal x-axis. - \(I_x\) is the moment of inertia about the component's own centroidal x-axis. - \(A\) is the area of the component. - \(d\) is the distance from the component's centroid to the composite centroidal x-axis.4. **Sum of Moments of Inertia:** - Sum the moments of inertia (including any adjustments from the parallel axis theorem) to get the total \(I_x\) for the composite section.By following this method, one can accurately determine the moment of inertia \(I_x\) for

Answered: Image /qna-images/answer/7f02ec82-713a-4e34-99e3-42b57cc2bfaf.jpg

Answered: W 8x40 C 8x13.75 Find lx bf

Engineering

Civil Engineering

W 8x40 C 8x13.75 Find lx bf

Materials Science And Engineering Properties

1st Edition

ISBN:9781111988609

Author:Charles Gilmore

Publisher:Charles Gilmore

Chapter12: Composite Materials

Section: Chapter Questions

Problem 12.13P

See similar textbooks

Similar questions

A bar having the cross section shown has been formed by securely bonding brass and aluminum stock. Taking h= 9 mm and using the data given below, determine the largest permissible bending moment when the composite bar is bent about a horizontal axis. Brass Aluminum 30 mm Modulus of elasticity Allowable stress h 30 mm h Aluminum 70 GPa 100 MPa The largest permissible bending moment is Brass 105 GPa 160 MPa 1.17 kN-m.
The composite section shown is made up of Channel and Wide Flange Steel section. Determine the properties of composite section. Channel (C 15 x 40) Wide Flange (W 18 x 158)
PROBLEM 2: The composite block shown carries a load P transmitted through an end bearing plate as shown. If the total load to be carried by the aluminum plates is to be half as the load carried by the brass core, what should the dimension h of each aluminum plate be? Brass core Rigid end plate (E = 105 GPa) Aluminum plates (E = 70 GPa) P FINAL ANSWERS h mm 300 mm 60 mm 40 mm h
For the composite bar indicated, determine the permissible bending moment when the bar is bent about a vertical axis. Aluminum stress is 100 %3D MPa, Brass stress is 160 MPa, Eb = 105 GPa, Ea = 70 GPa Brass 6 mm Aluminum 30 mm 6 mm -30 30 mm
ANSWER THE PROBLEM GIVE WHAT IS ASKED, SHOW YOUR SOLUTION, AND BOX THE FINAL ANSWERS. WRITE IT ON A CLEAN PAPER CLEARLY. I WILL GIVE THE FEEDBACK RATING AS POSSIBLE, YOU CAN ANSWER IT. THANK YOU
8. Two metal strips are securely bonded to a metal bar of 30 X 30 mm square cross section. Using the data given below, determine the largest possible bending moment when the composite bar is bent about a horizontal axis. I Aluminu Brass m Modulus of Elasticity 70 GPa 105 GPa Allowable Stress 100 MPa 160 MPa Brass Aluminimum Brass 30 mm 3. ww 9 30 mm
A bar having the cross section shown has been formed by securely bonding brass and ahumimum stock. Using the data given below, determine the largest permissible bending moment when the composite bar is bent about a horizontal axis. Aluminum Brass SO GPa Moduhus of elasticity Allowable stress 100 GPa 100 MPa 160 MPa M = kN-m 20 mm 20 mm Aluminum 20 mm Brass 46 mm 20 mm 46 mm
1. Three metal strips, each 40 mm height, are bonded together to form the composite beam shown. The modulus of elasticity is 210 GPa for the steel, 105 GPa for the brass, and 70 GPa for the aluminium. If the allowable bending stress for the aluminum (Gallow)al= 100 MPa, for the steel (Gallow)st 150 MPa and (Gallow)br=200 MPa for brass determine the maximum allowable intensit of w of the uniform distributed load. 2w 2m Aluminum Brass Steel 40 mm- 10 mm 10 mm 20 mm
Please show your complete solution l.
a) Determine the location of the centroid with respect to the point P; y = mm Submit part Unanswered b) Determine the moment of inertia l with respect to the centroidal axes. x106 mm*
Determine the y-bar centroid of the composite figure shown. Where: y = 20mm and x = 10 mm
Determine the y-bar centroid of the composite figure shown. Where x1%-68; x2=100 and y3D84 x1 x2 - y