Analysis of Beam Bending and Shear Stresses - ME Homework 17

This document provides solutions to a mechanical engineering homework assignment focusing on beam bending and shear stresses. The assignment addresses key concepts such as identifying the tension flange in a beam based on bending moment diagrams, determining sections with specific stress distributions, and calculating the point of inflection. The solution includes an analysis of bending moment diagrams to pinpoint areas of tension and compression and explains how gluing cards together increases bending resistance by preventing shearing forces. The homework covers topics from a structural mechanics course, and the solutions are presented with clear explanations and relevant figures. This homework provides students with a comprehensive understanding of beam behavior under load.

SOLUTIONS TO THE HOMEWORK QUESTIONS
QN 1) By eye inspection, the beam is likely to bend downwards such that the upper side will be
in tension while the lower part of the beam will be in compression. By sign convention, negative
bending moment occurs when the top fibers are in tension and the bottom fibers are in
compression (Litg.ac.in, 2018). Hence the tension flange of the beam is found on the top side of
the beam as illustrated in figure 1.
Top fibers in tension
Bottom fibers in compression
Figure 1: The cantilever bending (negative bending moment shown)

QN 2) (a) for the sections in the beam where tension is on the top and compression is on the
bottom, check sections with a negative bending moment (Litg.ac.in, 2018).
Hence from the graphics provided, it is found that the section with a span of 6’ is where the
above is happening (this is also indicated in figure 2)
B A
Figure 2: Shear and Bending Moment diagram

A-The point of inflection (where transition occurs from positive to negative bending moment
B- Section where negative bending moment is occurring (that is tension at the top and
compression at the bottom)
(b) This changes at the point where the second BM is zero (that is immediately after the 6’ span).
This is indicated in figure 2.
(c) We must first determine the bending moment expression for the whole beam span.
Now, by eye inspection, the curves are quadratic in nature hence quadratic equation is expected
(as the bending moment equation).
Therefore, according to Skyciv.com (2018), we determine the bending moment equation as
follows:
Bm= +200X2/2-[2700(x-18)-900x]
= 100x2-2700x-48600+900x
= 100x2-1800x-48600 0<x<18
Now, the point of inflection happens when the slope of the bending moment is zero, that is:
dBm/dx= 0
dBm/dx= 200x-2700= 0
200x= 2700; x= 2700/200= 13.5

Hence this occurs at the point x= 13.5
QN3) By gluing the cards together, we prevent sliding during bending of the cards. We therefore
overcome shearing force. Without this fastener (gluing) the cards would slide past each other
resulting in shearing and deformation. The fasteners (glue in this case) therefore act as a shear
resisting element (sliding is prevented and this is a shearing phenomenon).

Reference
Litg.ac.in. (2018). Shear force and Bending moment diagrams.[online] Available at:
http://www.iitg.ac.in/scifac/qip/public_html/cd_cell/chapters/CD-Cell.pdf [Accessed 29
Nov. 2018].
Skyciv.com. (2018). How to Draw Bending Moment Diagrams | SkyCiv. [online] Available at:
https://skyciv.com/tutorials/how-to-draw-bending-moment-diagrams/ [Accessed 29 Nov.
2018].