Integrated learning of engineering and mathematics modules

CDIO Conference 2009

our team

fan kee sengyoong yuen soo, nashatar singh,ng geok ling

Singapore Polytechnic

School of Architecture & the Built Environment Department of Mathematics & Science

problem

• in engg modules, formulae are given to students to solve engg problems

• the concepts and principles of some of these formulae are not explained to students in the engg modules as they are taught in math modules

• however, students can’t relate the math modules and the engg modules• hence they do not have a good understanding of some of the engg formulae

our motivation• to link engg and math modules using a

formulae booklet

CDIO Standard 3 integrated curriculum

CDIO Standard 7Integrated learning experience

• to realign the math content to make it more explicit in its applications to engg so that students are able to relate and apply mathematical concepts and principles to solve engineering problems

methodology

• module coordinators of engg modules were asked gathered the formulae used their modules• a total of 210 formulae – compiled into a

formulae booklet

• each formula in the booklet is indicated with a reference to a math module

• similarly in each math chapter, references to the formulae booklet are also indicated

examples from the formulae booklet

Ff

A

l

l

Module Name: Structural Mechanics (Engineering Module)Module Code: BE752YModule Coordinator: Rose HuangFormulae used:

1 Direct stress

2 Direct strain

3 Young’s modulusf

E

4 Bending stressxx

M yf

I

Linkage to mathematics module is shown in the yellow box.

Math ModuleIntegration (MS322Z, Chapter 4)

2NAI I A h 5 Moment of inertia

Math Module Integration (MS322Z, Chapter 8)

6 Euler’s buckling load

2

cr 2e

EIP

L

7 Deflection of beam

Math ModuleIntegration (MS322Z, Chapter 8)

There are 210 formulae in our formulae booklet (25 pages)

45wLv =

384E I

examples from the formulae booklet

example – math module

Example 2

Reaction at each support

wL=

2

Structural Mechanics: Finding Reactions

Total load

2

2

d v MSolve = where M = f(x)

EIdx

2

2

d y dya +b +cy = f(x)

dx dxChapter 8 Solving Differential Equations of the form

= wL

Math module: Reference booklet on Mathematical Modelling

Example 1 2

22

d ySolve = x + 2

dx

42x

y x Ax B12

Link to formulae booklet -page 3 Formula 7 (Structural Mechanics) and page 15 Formula 103 (Theory of Structure)

example – math module

To find M --- use the free body diagram below

Take moment about point C

Structural Mechanics: Free body diagram

)x(2

wL)

2

x)(wx(M

2wLx wxM =

2 2

2wM = (Lx x )

2

wL

2

example – math module

2

2

d v M= where M = f(x)

dx EI

Math module: Reference booklet on Mathematical Modelling

2 22

2 2

d v w d y(Lx x ) ------- it is of form = f(x) Eqn (1)

dx 2EI dx

Integrate wrt x

2 3dv w Lx x= +A Eqn 2

dx 2EI 2 3

3 4w Lx xv Ax B Eqn (3)

2EI 6 12

Integrate wrt x

example – math module

L dvwhen x , 0 as shown below

2 dx

Concept of boundary conditions as applied to the deflection at the mid-span of a simply support beam

To find the constant A, the boundary condition is:

That is, the gradient is zero when the deflection is maximum

Math module: Application of Differentiation MS3126 Chapter 5

Hence equation (2)

becomes

2 3dv w Lx xA

dx 2EI 2 3

2 3w L L 1 L0 ( ) ( ) A

2EI 2 2 3 2

3 3w L L0 A

2EI 8 24

3w 2L0 A

2EI 24

3LTherefore A

12

Math module: Simplification MS3126 Chapter 1

example – math module

To find B, the boundary condition is:

3 4w Lx xv Ax B

2EI 6 12

0 (0 0 0 ) Therefore B = 02

wB

EI

3 4 3w Lx x Lv x

2EI 6 12 12

Concept of boundary conditions at a support

becomes

Hence the deflection equation is

when x = 0, v = 0 i.e. no deflection at the support

Hence equation (3)

Maximum deflection occurs at the mid span i.e. L

x2

Hence,3 4 3w Lx x L

v x2EI 6 12 12

becomes

4 4 4

maxw L L L

v2EI 48 192 24

Math module: Substitution and Simplification MS3216 Chapter 1

example – math module 4 4 4

maxw 8L 2L 16L

v ( )2EI 384

4

maxw 10L

v ( )2EI 384

4

max5wL

v384EI

Link to formulae booklet -page 3 Formula 7 (Structural Mechanics) and page 15 Formula 103 (Theory of Structure)

Linkage to the formulae booklet.

When loading condition is changed ……….

When support is changed ……….

Carry out project work that may involve the use of these concepts to solve more difficult problems

Example 3 2

2

d y dySolve 4 + 5y = 60

dxdx

another example – math module

STRAINSECTION SIMPLIFIED STRESS

2

00.9

z z k

d d

0.5 0.250.9

Kz d

Math module needs to fill up the ‘gaps’ in engg modules

Filling up the ‘gaps’ in engg module

Example: Concrete Design

another example – math module

Missing basic concepts from from the entire course

( ) b

u lA ax dA x y y dx

Math modules need to be realigned to include important basic concepts

Example: Concept of dA

• hence, there are cross references of engg and math modules

• some of the concepts and principles of engg formulae are explained in math modules more explicitly• hence this will promote students’ understanding of engg content better

SURVEY FINDINGS

.

Carried out a survey last year on 135 students

Each student was given a copy of the formulae booklet

• 90% of the students felt that the formulae booklet helped them learn engineering modules better

• 85% of the students felt that the booklet helped them relate better how mathematical concepts are applied in engineering modules

• 77% felt that, with the help of the booklet, they were motivated to learn mathematics

• 93% of the students felt that it was very convenient for them to refer to the booklet whenever they needed the formulae

• 81% felt that they would use the booklet in their work or in their further studies after graduation

room for improvement

Students want more formulae to be included in the formulae booklet – from Geomatics and Structural Analysis

*** The compilation of the formulae booklet is creative and a task well done.

The meaning of each term or symbol used in the booklet should be given.

Provide soft copy of the formulae booklet with the necessary links to engineering and math module.

Provide reference booklet e.g. mathematical modelling for self-directed learning.

2

2

d v M=

dx EI

the road ahead

• time consuming – not all all formulae have been linked

• need to realign math modules to meet the requirements of engg modules

• some formulae in the booklet could not be linked directly

• further improve on the layout of the formulae booklet

Q & A

Thank You