1. Overview of Engineering Analysis
San Jose State University
Department of Mechanical Engineering
ME 130 Applied Engineering Analysis
Instructor: Tai-Ran Hsu, Ph.D.
Chapter 1
Overview of Engineering Analysis
2018 edition

2. Chapter Learning Objectives
● To learn the concept and principles of engineering analysis, and the vital roles that
engineering analysis plays in professional engineering practices
● To learn the need for the application of engineering analysis in three principal
functions of professional engineering practices in: creation, problem solving and
decision making.
● To illustrate the critical needs for engineers solving problems that relate to protection
of properties and public safety, and also the needs for engineers making decisions
in real-time situations that often involve grave consequences.
● To learn the roles that mathematics play in engineering analysis, and the ability to
use mathematical modeling in problem solving and decision making in dealing with
real physical situations.

3. What is Engineering Analysis?
Engineering analysis involves the application of scientific principles and
approach that often use mathematical modeling as a tool to reveal the
physical state of an engineering system, a machine or device or structure
under study.
Application of Engineering analysis also include electric circuit design,
derivation of algorithms for computer programming, etc. It is an integral
part of the professional practice of ALL engineering disciplines.
Engineering analysis is a vital TOOL for practicing engineering professionals in performing their principal duties in:
Creations
Decision making
Problem solving

4. Engineers create:
“Scientists DISCOVER what it was,
Engineers CREATE what it is not”
Engineers create “what it is not” in DESIGN to satisfy human needs and
sustain high living standard for all human kind:
Greatest Engineering Achievements of the 20th Century
as selected by the US Academy of Engineering
1. Electrification* Highways
2. Automobile* Spacecraft*
3. Airplane* Internet
4. Water supply and distribution 14. Imaging
5. Electronics Household appliances*
6. Radio and television Health technologies
7. Agriculture mechanization* 17. Petroleum and petrochemical technologies
8. Computers Laser and fiber optics
9. Telephone Nuclear technology*
10. Air conditioning and refrigeration* High performance materials
* With significant mechanical engineering involvements

5. Engineers make DECISIONS – at all times, and often crucial ones:
Decisions are required in:
● Design – Configurations of engineering systems
Selection of design methodology, materials and fabrication methods
Assembly, packaging and shipping
● Manufacturing – Tools and machine tools
Fabrication processes
Quality control and assurance
● Maintenance – Routine inspections and Procedures
● Unexpected cases with potential grave consequences –
Change of customer requirements
Malfunctioning of machines and equipment
Defections in products
Examples on Critical Decisions by
Engineers on what to do
if flaws or cracks appear
on the surfaces of:
● Pressurized pipelines, e.g. the
Alaska Pipelines and San Bruno
Gas Pipeline burst or
● A jumbo jet airplane

6. Engineers solve Problems – often in ways like fire-fighting:
Problems relating to:
Design fault and ambiguity
Manufacturing disorder
Malfunction of equipment
Inferior quality in production
Run-away cost control
Resolving customer complaints and grievances
Public grievances and mistrust

7. are of PHYSICAL nature too
All TASKS relating to:
Creation
Decision making
Problems solving
are of PHYSICAL nature
The required ANSWERS
are of PHYSICAL nature too

8. Engineering Analysis by Mathematical Modeling
Engineering Problems
(Physical)
Mathematical
Modeling
Mathematical
Formulation
Engineering
Analysis
Mathematical
Analysis
Translate engineering
problems into math
form by:
1) Idealizing physical
situations.
2) Identifying idealized
physical situation
with available math
representations
3) Formulate math
models, e.g., expres-
sions, equations.
Desirable direct approach
Not
Possible!
Mathematical
Solutions
Unavoidable Approach
Solution to
Engineering Problems
(Physical)
Translation Math
to Physical
Situation
Conclusion: Math plays a principal role as a servant to
Engineering (the Master) in engineering practices

9. Mathematical Modeling
Math modeling is a practice involving the translation of physical (engineering)
situations into mathematical forms, and vice versa.
Tool Box for Engineering Analysis:
● Empirical formulas
● Algebraic equations and formulas from textbooks and handbooks
● Differential and integral equations with appropriate conditions
fit to the specific problems
● Numerical solutions, e.g., by finite element method (FEM) or
finite difference method (FDM).
Many mathematical formulas and expressions are available in handbooks, e.g.:
“Mark’s Standard Handbook for Mechanical Engineers,” 10th edition,
Edited by Eugene A. Avallone and Theodore Baumeister III, McGraw-Hill,
New York, 1996, ISBN

10. Example of Engineering Analysis by Empirical Formula
Estimate pressure drop in fluid flow in pipes:
Fluids flow in pipeline requires pressure supplied either by pumps, fans or gravitation. Pressure drop ∆P is
The basis for selecting a powerful enough pump for the intended fluid flow in a pipeline.
Unfortunately, it is too complicated to be computed. But engineers must have this information to design the pipe flow.
Following empirical formula is often used: P2
Pump P1
Pipe flow
where ρ = mass density of the fluid, v = average velocity of the fluid flow, L = length of the pipe, D = diameter of
the pipe, and f = friction factor from Moody chart
The friction factor f with the values available from the Moody chart is derived from experiments.
where f = Moody friction factor , v = average velocity of fluid flow,
D = diameter of the pipe, Rb = radius of the pipe bend, and
kb = the bend loss coefficient.
Numerical values of the bend loss coefficient kb are available in a handbook:
The estimated pressure drop ∆P is then used to design
the pump or fan to drive the fluid through a pipeline.

11. Examples of Using Algebraic equations and formulas from textbooks and handbooks in Engineering Analysis
Determine the dynamic force induced by changing velocity of moving solid using
the Newton’s Law:
Induced force (F) = Mass of the moving solid (M) x Acceleration (a) or Deceleration (-a)
2) Determine the induced stress to a solid bar by applied force using the Hooke’s Law:
Induced stress (σ = F/A) = E x Induced strain (ϵ = ∆L/L)
where F = applied force, A = cross-sectional area, E = Young’s modulus (material property)
∆L = elongation or contraction of the bar, L = original length of the bar
Determine the velocity of fluid flow in a pipe (nozzle) with variable cross-sections
using continuity law: A1 A2 V1 V2

12. Differential Equations in Engineering Analysis:
Examples of using Differential and Integral Equations in Engineering Analysis
Differential Equations in Engineering Analysis:
Determine the rate of solvent A with lighter concentration diffuses into solvent B with
heavier concentration :
where C(x,t) = concentration of A at depth x and time t, D = diffusivity
of diffusion of A to B
2) Integral Equation in Engineering Analysis:
Solve for function f(x) in the equation:
Solution:

13. Numerical Solutions for Engineering Analysis
Numerical solution methods are techniques by which the mathematical problems that are associated with engineering analysis cannot be solved by analytical methods, such as by the above methods in the “tool box.”
Numerical techniques have greatly expanded the types of problems that engineers can handle in: (1) Solving nonlinear polynomial equations, (2) Graphic expressions of functions, (3) differential equations by “finite difference methods” and (4) Problems with complicated geometry, loading and boundary conditions, such as by the “finite element methods.”
Example: To determine the stress induced in the plate with the following loading condition: w F d D F F
Plain solid plate: EASY
Plate with a small hole of diameter d is a much, much harder case
Numerical solution by
Finite element method:
Principal tasks in numerical methods for engineering analysis is to develop algorithms that involve arithmetic and logical operations so that digital computers can perform such operations.

14. The Four Stages in General Engineering Analysis
Engineers are expected to perform “Engineering analysis” on a variety of different cases
in their careers. There is no set rules or procedure to follow for such analyses.
Below are the 4 stages that one may follow in his (her) engineering analysis.
Stage 1: Identification of the physical problem – specification of the problem:
To ensure knowing what the analysis is for on:
● Intended application(s)
● Possible geometry and size (dimensions)
● Materials for all components
● Loading: range in normal and overloading; nature of loading
● Other constraints and conditions, e.g., space, cost, government regulations
Stage 2: Idealization of actual physical situations for subsequent mathematical analysis:
Often, the engineer needs to make assumptions and hypotheses on the physical
conditions of the problem, so that he (she) can handle the analysis by his (her)
capability with the “tools” available to him or her.
Stage 3: Mathematical modeling and analysis: by whatever means he (she) believes applicable
e.g., solution methods from handbooks, computer software, company handbooks or
own derived formula and equations, including differential equations, etc..
Stage 4: Interpretation of results – a tricky but important part of engineering analyis.
To translate the results of math modeling with numbers, charts, graphs to physical
sense applicable to the problem on hands

15. * If the product is a structure, or components
GENERAL ENGINEERING DESIGN PROCEDURE with 4 stages of engineering analysis
Stage 1: Understand the physical
problem
Stage 2: Idealization for
math modeling
Stage 3: Math modeling
& analysis
Stage 4: Interpretation
of results:
CHECK IF ALL REQUIRED
CRITERIA* ARE MET
* If the product is a structure, or components
requiring sufficient strength, then the concept
of safety factors will be Included in the criteria,
as will be demonstrated in the Example.

16. Example on Application of Engineering Analysis: Design of a Bridge across a Narrow Creek:
Stage 1: Description of the Physical Conditions:
The required short bridge is specifically designed
to handle limited local traffic over a narrow creek.
The span of the bridge is 20 feet, and the maximum
load for the bridge is 20 tons (or pounds).
The simplified geometry and dimensions of the
bridge are illustrated in:
Engineers decide to use two (2) I-beams made of steel
to support of the bridge structures for the following two reasons: (1) the bridge is built across a narrow creek and it is mainly subject to bending loads. I-beams are best suited for carrying this type of loads, and (2) the primary concern for this structure is “public safety.” Steel is common structure material with reliable strength, and I-beams are widely available with moderate cost.
However, design engineers need to find the adequate size of these beams from suppliers with STANDARD dimensions.
Their first trial is to use the I-beams with the following dimensions set by the supplier (you may find these dimensions from handbooks): H1=12”, H2=10.92”, b1=5” and b2=0.35”.
Also: Max. tensile strength= 75,000 psi and max. shear strength=25,000 psi (handbooks)

17. Stage 2: Idealizations of physical situation in order to use “Simple Beam theory”
for mathematical analysis:
Because the primary design consideration of the structure is its capability of carrying bending
Loads from the intended traffic. Engineers realize that “simple beam theory” that they learned
in the “strength of materials” class (e.g., SJSU CE 112 course) would be available to calculate
the maximum bending stresses in the I-beams induced by the expected loading.
But the formula that they had learned in these courses only deal with the following simple cases: P
w lb/length
Simply-supported: ● ● ● ●
w lb/length
Rigidly held support:
None of the above available conditions resembles
(and therefore applicable) to the real situation that
he (she) needs to deal in the real situations
Therefore there are needs for him (her) to idealize the real
Situations, so that he (she) can use the available formula
in textbooks or reference books derived for simple-beam bending as show above.

18. Stage 2: Idealizations of physical situation in order to use “Simple Beam theory”
for mathematical analysis – cont’d:
Following are many idealizations that engineers need
to make in order to use “simple-beam theory:”
The maximum load applied to the bridge is equally
carried by two identical I-beams
The weights of the I-beams and other materials are
neglected (This is obviously a serious violation of reality!
We make this idealization nonetheless in order to simplify
the subsequent mathematical manipulations).
Each I-beam carries half of the total load, i.e. 20,000 lbf.
Assume that each of the 4 wheels carries equal amount of load (another questionable
assumption).
By judgment, the worst condition to be considered is when the vehicle is at the mid-
span position . (appears to be the only reasonable assumption!)
One end of the beam is hinged to a fixed anchor and the other rests on a roller.
The I-beams can thus be considered to be simply supported (as engineering
mechanics textbooks often indicate).

19. for the present engineering analysis:
Stage 3: Mathematical analysis Use available formula for “Simple Beam theory”
for the present engineering analysis:
One-side front wheel load:
One-side rear wheel load:
Idealized to simple beam in bending
Real problem
Simulated simple beam bending
The maximum bending stress in one I-beam is:
Maximum normal stress along the longitudinal direction
of the I-beam
at the center of the I--beam cross section,
Where M = maximum bending moment
c = half the depth of beam cross section
I = area moment of inertia
The maximum shearing stress is:
Numerical results:
σn,max = 26,740 psi, and
σs,max = 2744 psi
The maximum deflection at the center span is: 0.84 in. – not a critical factor in this design
Where V = maximum vertical shearing force
b2 = width of the rib of an I-beam
Q (0) = statical moment at the center of beam cross section

20. Stage 4: Interpretation of Results:
The max. induced tensile stress in the I-beam to be: σn,max = 26,740 psi, and
The max. induced shearing stress in the I-beam to be: σs,max = 2744 psi
We obtained the numerical results from
Stage 3 using simple beam theory:
What shall we do with these numbers for our design problem???
Recall: We were given in Stage 1 of this analysis that the maximum tensile strength of the
steel I-beams to be:75,000 psi, which is much higher than the numerical results we computed.
So, the selected 12” I-beams should be safe enough for the intended loading because both
the computed σn,max and σs,max are LESS than the maximum strength of the material, or is it?
It would have been all right with the above assessment. However, because of the
IDEALIZATIONS that we made in Stage 2 of the analysis, the maximum induced stresses
in the beam may be a lot higher than what we have computed. (WHY??) Yet such idealizations
were necessary in order for us to use simple beam theory to produce these numerical results.
COMPENSATION for the “convenience” we get in Stage 3 analysis must be given –
The Safety Factor (SF) as we introduced in the book. In this case the SF is equal to:
SF = Ultimate tensile strength (of the material)/maximum induced stress = 75000/26740 = 2.8,
which is far less than 5 or 6 for this type of structures
We thus conclude that the use of 12” I-beams in this design is NOT safe enough!!
Question: What would you do if you were the engineer working on this design project??

21. What More Can be Done to Make the Design Analysis of This Bridge More Realistic
Making the Stage 2 of the analysis more realistic (and thus less idealistic) by doing the following:
Include the weight of the steel beams in the analysis.
Include the weight of the concrete pavement road surface, say: 20 feet long x 12
feet wide and 6 inches thick.
(3) With realistic load distributions on front and rear wheels
You may still use the formulas derived from “simple beam theory” but your analytical solution will be much more realistic. What differences in the numerical solutions will you get with the inclusion of conditions in (1), (2), and (3) in your analysis?

22. On Safety Factors in Engineering Analysis Dealing with Structures
Safety Factors (SF) is defined as:
SF = Ultimate tensile strength (of the material)/maximum (tensile) stress induced in the
structure
Typical Safety Factors for Engineering Analyses with Structures
There is NO rule to determine SF. In general, the more sophisticated analyses (with less idealizations
in Stage 2), and thus more RELIABLE analytical results, the lower SF would be applied. Public safety
is also a factor in determining the SF in the analysis. It explains why lower SF is used in aircraft design,
yet higher SF are used in pressure vessel design analysis .

23. Selected Engineering Case Studies
“Engineering is a profession, not just an occupation.” Engineers are responsible for public
safety and social welfare and justice too. Negligence in their duties may result in devasta-
tion to the public, as will demonstrated by the following selected case studies: Only sound
engineering analysis can mitigate such tragic happenings.
Case 1: Research and analysis on this engineering case study by response
to the following particular queries on the devastating “gas pipeline burst in San Bruno,
California in 2010 :
What really happened in this accident?
What are the consequences of this engineering disaster?
What was the cause of the accident relating to engineering negligence?
What were the loss of properties and human lives by this accident?
What the owner of the pipeline – PG&E has been doing in compensations to the victims
and remedial actions taken to avoid future similar occurrence?
If you were a senior engineering manager at PG&E, what would you do to prevent
the recurrence of the tragedy?
How can engineering analysis help?
Case 2: Crash of a DC 10 jet passenger plane over the Chicago O’Hare
airport on May 25th, 1979 as shown in the picture:
What would you, as an engineer or engineering manger do to avoid
recurrence of such tragic happenings in the future?

24. Self-Studies on Chapter-End Assignment
Read the Example on Application of Engineering Analysis on a bridge on P. 9.
Conduct an engineering analysis on the above example but include the weights
of the steel structure and the required concrete road surface for the bridge.
Remind you that you do not always have the information and conditions given in
your design analyses. You, as an engineer, needs to make reasonable and logical
assumptions on these missing information based on available reference “tools”
available to you.
3. Be prepared to answer the question on the significance of “Safety Factor” used in
a design analysis of a structure or machine component. What are the fundamental
principles for determining the numerical value of this factor?
Explain why a SF = 4 is used in pressure vessel design by ASME design code, yet
SF = 1.2 is used in aircraft structure design.
Be prepared to offer example of engineers making decisions and solve problems
based on your personal experience.