University Assignment: CE 2C04 Assignment 4 Solution - Winter 2019

This document presents a comprehensive solution to a mechanical engineering assignment (CE 2C04, Winter 2019) focusing on structural analysis. The solution addresses multiple problems, including the design of a steel beam, considering bending, shear, and deflection criteria. It determines the minimum beam height to satisfy these requirements and verifies the design at critical cross-sections using maximum shearing stress criteria. The assignment also analyzes a cast iron material using Mohr's criteria to determine failure under plane stress states. Additionally, it calculates the maximum load for an aluminum column, considering different lengths and applying Euler's equation for buckling analysis. The solution includes detailed calculations, formulas, and plots to illustrate the concepts and results. References are provided for the methodologies used.

Assignment 4
By
Student’s Name
Code + Course Name
Professor’s Name
University Name
City, State
Date

Question 1
Solution

Thus, the minimum height for a, b and c is estimated h= 320.75mm
At the ssectionat the support A, the overallshear force is given as 10kN. Thus, the maximum sher
stress is computed as (Ashby, Shercliff and Cebon 2018)
3 x 10 x 103
2 x 320.75 x 24 = 1.95 N/mm2
Also,
Stress < 0.45 x 200 =90N/mm2
Thus, the section is OK.
At the section of the Maximum Bending Moment which is the b/wfree end and A, then shear
force is =0.
Hence, the section is ok as well.
Furthermore, the overallsection adjusted at the right left the maximum shera force at the support
B is 14kN.
Thus, the maximum shear stress is computed as
3 x 14 x 103
2 x 320.75 x 24 =2.75N/mm2
Comparing with the < 0.45 x 200 = 90N/mm
Hence, the station is depicted as ok.
Question 2

A cast iron material with the following strengths
σT = 80 MPa and σC =180 MPa . For each of the plane stress states shown and using Mohr’s
criteria, either decide if the element fails or not (parts (a) and (b)) or
determine the normal stress σo at which failure of the component should be expected (part (c)).
Solution
Given that
σT = 80 MPa & σC =180 MPa,
Then, the criteria for failure can be determined as follows
a) The determination for the stress state in this category mainly illustrated as indicated
below

Furthermore, the principle stresses can be analyzed using the given stresses (Gratchev and
Sassa 2015).
b) The analysis for this section mainly represented as indicated in the figure below

c) The stresses analysis for the section often represented as indicated below

Question 3
Determine the maximum possible load for the following column, assuming
that the column is made of aluminum (E = 70 GPa) with a yield of 220 MPa.
a) When the column is 6m long
b) When the column is 3m long
c) At what length does the axial load switch from being governed by
axial compression to Euler’s equation?
d) Create an allowable load vs. length plot for the column
Note: If no information is given for support conditions or bracing, the

default assumption is that the column is pin-pin connected with no bracing.
All dimensions in mm.
Solution
The above figure can be drawn as shown below
Area is computed as
Area=2[ 8 x 14+1000 x 6+43 x 6]=1832 mm 2
Also, Ixx is given as
Hence, Ixx= 2.302 x 1 06 mm 4
The analysis of the Iyy is given using the figure below

Thus,
Depth of NA (y) = ∑ AR
∑ A
= (8 X 14)+(100 X 6)x 50+(34 x 6) x 97
( 8 x 14 )+ ( 100 x 6 ) +(34 x 6)
=55.33mm
Furthermore,

Also, the radius of gyration is given as follows
a) Assuming the column length is 6m
Then, the solution is computed as represented below

Preferably, the behave of the column will be depicted as the one for the long column as per euler
analysis. Thus, it is computed as follows
Converting the answer above to kN gives
Answer = 44.177kN
b) Also, provided the column length is 3m the analysis can be calculated as follows