Mechanical Engineering Case Studies and Calculations

Table of Contents
1. Case Study A...........................................................................................................................2
1.1 Question 1.........................................................................................................................2
1.2 Overview of the Beam......................................................................................................4
2. Case Study B............................................................................................................................7
2.1 Question 1.........................................................................................................................7
2.2 Question 2.........................................................................................................................8
2.3 Question 3.........................................................................................................................8
3. Case study C..........................................................................................................................11
3.1 Question 1.......................................................................................................................11
3.2 Question 2.......................................................................................................................13
4. Case study D..........................................................................................................................15
4.1 Question 1.......................................................................................................................15
4.2 Question 2.......................................................................................................................16
4.3 Question 3.......................................................................................................................17
5. References..............................................................................................................................18
6. Appendix................................................................................................................................19
1

1. Case Study A
1.1 Question 1
a) Reaction forces
Here, summation of horizontal forces are zero and summation of moments are zero.
Take moment about point A and point B.
Calculate RD and RA
Reaction force at point A, (RA) = 82.5 kN.
Reaction force at point D, (RD) = 77.50 kN.
Here, summation of vertical forces are zero.
Find the shear force at Point A, B, C and D (QA, QB, QC, and QD)
2

After that, find the bending moment at Point A, B, C and D (MA, MB, MC, and MD)
The calculations are added in appendix.
b) Shear force diagram
It is given in below diagram.
c) Bending moment diagram
The shear force and bending moment diagrams are shown below.
3

d) Max S.F and B.M
From the calculation done, the maximum shear force value and the maximum bending
moment value is found.
Maximum shear force value = 82.5 kN.
It acts at the point “A”.
Maximum Bending Moment value = 85 kN.m.
It is found in Point “C”.
1.2 Overview of the Beam
What is Beam?
Beam is a mechanical element. It is used to support the loads. Mostly it has a horizontal
orientation, in some cases we can see this at an inclined positions. In general, vertical loads and
moments are act on this element. And in some rare cases horizontal loads also may act on this
element. In other words, beam is a structural element. Its length is higher than its cross-sectional
dimensions like width and thickness. Also it undergoes to the lateral loading (Zhang et al. 2014).
Types of Beams
Beams are classified by many factors like type of support, Cross section etc. But
generally beams are classified according to the type of support used. In this section, the brief
overview of all five types of beams are shown.
Type Diagram Commercial
Application.
Cantilever Beam Aircraft wings,
& Balcony
support
4

Simply
Supported Beam
Bridges
Continuous
Beam
Bridges
Fixed Beam Rigid Structural
elements
Over hanging
Beam
Balcony
Types of loadings
Type Diagram
Point load
Uniformly Distributed Load
Uniformly varying load
Bending moment diagram and Shear force diagram shape
In this section, the Bending moment diagram and Shear force diagram shapes are drawn
for various types of loads acts on the various types of Beams.
5

Calculations
6

2. Case Study B
2.1 Question 1
a) Finding speed for developing the gravity
In this kind of space stations, the centripetal force developed by the rotary motion acts similar to
the gravitational pull.
So
Here the r= 0.9 km or 900 m
Centripetal acceleration a = 9.81 m/s2
According to this formula, the ring must rotate at 1 rpm in counter clockwise direction to
develop the centripetal acceleration as 9.81 m/s2.
Here, w= (2*pi*N)/60.
Using this, N value is found.
The calculation for this is added in appendix.
7