Excel Homework

College of Engineering and Computing

Department of Civil and Environmental Engineering

CGN 2420 - Computer Tools for Engineers

HOMEWORK 2:

Recommended Practice:

Chapter 5: 5.1, 5.2, 5.3, 5.4, 5.5, 5.8

Mandatory Problems:

1.- Given the following matrices and vectors:

𝑉 = 1 6

−4 8

𝐴 = 2 1 7 6 3 9 4 −4

𝐵 = 1 3 2 5 2 6 2 −8

𝐶 = 2 1 11 7 1 9 −9 0 1 12 7 1 2 5 1 8

For each operation that can be performed, determine the result. Otherwise, explain the reason why the operation cannot be done. a) BT transpose of matrix B.

b) B . V multiply matrix B by vector V.

c) B-1 inverse of matrix B.

d) |C| determinant of matrix C.

e) C-1 inverse of matrix C.

f) AT+ B add matrix A transposed to matrix B.

g) V . B multiply vector V by matrix B.

h) AT . V multiply matrix A transposed by vector V.

i) C-1 . V multiply the inverse of matric C by vector V.

j) (BT.B).C multiply transpose of matrix B by matrix B, then multiply by matrix C.

2.- A truss structure is composed of five members and is subjected to two loads as shown in the figure. Given the geometric and material properties of each member, the displacements of the two unsupported nodes can be determined by solving the following equilibrium equations

3.75 × 10 5 1 0 0 1 5 0 −4 0 0 5 −1 0 −4 −1 5

𝑢 𝑢 𝑢 𝑢

= 500

0 0

1000

Determine the nodal displacements u1, u2, u3, and u4 by:

a) Solving the system of equations using the inverse of the coefficient matrix. b) Using Cramer’s Rule.

Due Date: Tuesday, February 6th, 2017 Please submit your Homework on time to the corresponding gmail account: [email protected] Section RVC

[email protected] Section U01

Use only ONE Excel file, with problem 1 in one spreadsheet and problem 2 in

another one. Save the file with your NAME, LASTNAME and HW number.

In the subject of your email write your Name and Homework number.