Determine the orientation of the principal axes having an origin at point C, and the principal moments of inertia of the cross section about these axes using Mohr’s circle. The image depicts a 3D representation of an L-shaped structural component. It consists of two perpendicular metal plates connected in the form of an L. The dimensions of the component are clearly indicated with measurements:- The vertical plate has a height of 100 mm.- The horizontal plate has a length of 80 mm.- The thickness of the metal is 10 mm for both plates.The L-bracket is positioned in a coordinate system where the origin (C) of the axes is marked at the internal corner where the two plates meet. The positive y-axis extends upwards along the vertical plate, whereas the positive x-axis extends to the right along the horizontal plate. This setup highlights how such components can be analyzed in terms of dimensions and spatial orientation within engineering and physics contexts.

Draw the free-body diagram of the given figure. Calculate the moment of inertia about the x-axis. Ix=140×10312+210×100312+10×100452=5.7283×106 mm4 Calculate the moment of inertia about the y-axis. IY=1403×1012+2100×10312+100×10752=13.55×106 mm4 Calculate the moment of inertia about the xy-axis. Ixy=0+0+10×100-7545+0+1010075-45=-6750000 mm4 Calculate the coordinates of the center O. Ix+Iy2, 0=5.7283×106+13.55×1062, 0=9.639×106, 0 Calculate the coordinates of the reference point A. Ix, Ixy=5.7283, -6.75106 Calculate the radius of the circle. R=OA=106×9.369-5.72832+-6.752=7.669×106 Draw the circle as follows. Calculate the maximum moment of inertia. Imax=9.639+7.669106=17.308×106 mm4 Calculate the minimum moment of inertia. Imin=9.639-7.669106=1.97×106 mm4 Calculate the orientation θp2. tan2θp2=6.759.639-5.7283θp2=29.95∘ Calculate the orientation θp1. 2θp1=180∘-2θp2=180∘-229.95∘=120.1∘θp1=60.05∘

Answered: Determine the orientation of the…

Engineering

Civil Engineering

Determine the orientation of the principal axes having an origin at point C, and the principal moments of inertia of the cross section about these axes using Mohr’s circle.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

Determine the orientation of the principal axes having an origin at point C, and the principal moments of inertia of the cross section about these axes using Mohr’s circle.

The image depicts a 3D representation of an L-shaped structural component. It consists of two perpendicular metal plates connected in the form of an L. The dimensions of the component are clearly indicated with measurements:

- The vertical plate has a height of 100 mm.
- The horizontal plate has a length of 80 mm.
- The thickness of the metal is 10 mm for both plates.

The L-bracket is positioned in a coordinate system where the origin (C) of the axes is marked at the internal corner where the two plates meet. The positive y-axis extends upwards along the vertical plate, whereas the positive x-axis extends to the right along the horizontal plate. This setup highlights how such components can be analyzed in terms of dimensions and spatial orientation within engineering and physics contexts.

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