chapter 3 - Bentham Science

20 Applications of Spreadsheets in Education The Amazing Power of a Simple Tool Nelson Lam
left to right using the fill right command. The solution of eigenvalues (modal natural periods)
and eigenvectors (mode shapes) in a dynamic modal analysis could also be calculated by Excel
as illustrated in Section 2.4.2. The spreadsheet solution features iterations through populating the
worksheet with column arrays from left to right (using the fill right command). Every iteration
commences at the column array on the left and then ends at the column array on the right. In
perspective, the forward marching algorithm, the calculation and plotting of the response spectra
and the solution of the modal periods and mode shape vectors have all been accomplished by fully
exploiting the standard row and column operations in Excel. Further details of programming in
Excel for structural dynamic analysis is given in Section 2.4. Much fuller details of algorithm
development for structural dynamic analysis and simulations are presented in [1, 2]. The use of
Excel for analysis of cracked reinforced concrete cross-sections based on the fiber-element approach
is presented in [3]. Results obtained from the latter program for analysis of cracked reinforced
concrete can be compared with recommendations in [4, 5].
Another important attribute of Excel suitable for engineering education and training is its transparency.
Conventional programming languages such as Fortran, C++, or Visual Basic present the
program algorithm in the usual text format, effectively delivering information in one dimension.
Elaborate algorithms of large computer programs are therefore difficult to follow. In contrast, an
algorithm in Excel is the worksheet itself, thereby delivering information in two dimensions. Algorithms
in Excel can be introduced by a sequence of worksheets, each of which presents a snapshot
of the progressive development of a spreadsheet program (from a blank sheet into its final form).
The presentation of a worksheet for illustration to the user can be enhanced in a number of ways
including the use of annotations, the coloring of cells (to identify which are the ones for the input
of data). Thus, a program in Excel can be introduced to users without the need of a user’s
manual. Details of every step in the computations are evident in the spreadsheet itself if only row
and column operations have been used. This enables users to make modifications to the program
customizing specific needs, while having full knowledge of its operations as well as the underlying
computations. The blackbox syndrome of a computer program is hence eliminated.
2.2 Beam Analysis (Elementary Level)
The teaching of elementary structural mechanics using Excel may begin with the cantilever beam
for illustration purposes. For any location on the beam which is measured at distance x from its
free-end, values of 〈x−xi〉 = max(x−xi, 0) are calculated where subscript i denotes the position
of the applied point force and xi is the distance of the point force Fi measured from the free-end.
Observe that when x−xi is a positive value, 〈x−xi〉 is taken to be equal to x−xi, or else 〈x−xi〉
is taken to be equal to zero. This formulation allows the calculation of shear force and bending
moment values to be generalized into simple one-line expressions as shown by Equations (2.1a)
and (2.1b) – based on the usual free-body diagram principles and the resolving of forces and taking
moments about the point of interest.
SF(x)=
BM(x)=
N
∑
i=1
N
∑
i=1
Fi〈x−xi〉 0
Fi〈x−xi〉 1
(2.1a)
(2.1b)