calculate the moments of inertia with respect to both centroidal axes for the areas shown Section 8.4 Moment of Inertia5"5"8HY(a)1"Y10"X-X-2"6"2"(c)PROBLEM 8.9Composite Areas8.8

Area of flange A1 = (6+2+6)×2=28 in2 Area of web A2 = 10×2=20 in2 Since the given section is…

Answered: calculate the moments of inertia with…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Question

calculate the moments of inertia with respect to both centroidal axes for the areas shown

Section 8.4 Moment of Inertia
5"
5"
8H
Y
(a)
1"
Y
10"
X-
X-
2"
6"
2"
(c)
PROBLEM 8.9
Composite Areas
8.8

Expert Solution

Step 1

Area of flange A₁ = $(6 + 2 + 6) \times 2 = 28 i n^{2}$

Area of web A₂ = $10 \times 2 = 20 i n^{2}$

Since the given section is symmetrical, centroid along x-axis is 0 i.e. x₁=x₂=0

Centroid of flange y₁ = $\frac{2}{2} = 1 "$

Centroid of web y₂ = $2 + \frac{10}{2} = 7 "$

Centroid of complete section:

$\begin{array}{rcl} Y & = & \frac{A_{1} y_{1} + A_{2} y_{2}}{A_{1} + A_{2}} \\ = & \frac{28 \times 1 + 20 \times 7}{28 + 20} \\ = & 3.5 " \end{array}$

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

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, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions