Math-cad

College of Engineering and Computing

Department of Civil and Environmental Engineering

CGN 2420 - Computer Tools for Engineers

HOMEWORK 6:

Recommended Practice (from textbook Mathcad 15)

Chapter 2: 2.12, 2.16, 2.19, 2.20

Chapter 3: 3.9, 3.12, 3.18

Chapter 8: 8.2, 8.4, 8.6, 8.7

Mandatory Problems:

1.- Take your Excel textbook and read application in page 44 named FLUID STATICS. Implement this

worked example in Mathcad.

a. Define variables (use units)

b. Write equations

c. Solve for the pressure in all cases (give your results in Pa and atm)

d. If possible insert pictures (you have one picture in the word file posted on blackboard).

2.- Problem 3.20 from Mathcad textbook: A Linear Interpolation Function.

3.- The natural frequencies of a 3 degree of freedom spring – mass system are given by the equation

𝛼 − 5𝛼 + 6𝛼 − 1 = 0

where 𝛼 = , and m is the mass,  is the natural frequency, and k is the spring stiffness.

Find the natural frequencies of the spring-mass system shown if m = 2.5 kg and k = 100 N/m.  is dimensionless. Hint: find 𝛼 possible values first, and then solve for the corresponding natural frequencies. Do not use the latter m in Mathcad for the mass, since you will be overwriting the unit for meters, you could use mo as example. 4.- The functions y and p are defined by:

𝑦(𝑥) = 3𝑥 − 20 and 𝑝(𝑥) = 200 − 11𝑥

a) Sketch the graphs in Mathcad for values of x between 0 and 10. b) Find the coordinates of the points of intersection in this range. c) Find the area bounded by the two curves and the vertical axis (explore using the definite

integral in the calculus toolbar). 5.- The figures below show a uniform beam subjected to a linearly increasing distributed load (a) and the corresponding beam deflection (b). The beam deflection y(x) can be computed with the following equation:

𝑦(𝑥) = 𝑤

120𝐸𝐼𝐿 (−𝑥 + 2𝐿 𝑥 − 𝐿 𝑥)

Where E is the beam modulus of elasticity and I the cross section moment of inertia. For E = 5x104 kN/cm2, I = 3x104 cm4, L = 600 cm, and wo = 2.5 kN/cm.

a) Plot the deflection curve of the beam (0 ≤ 𝑥 ≤ 600). b) Use a solve block in Mathcad to find the largest deflection of the beam and the location

(x value) where this occur. Please print your homework in a PDF file. Submit both, the Mathcad and the PDF file through Canvas. Save files with your NAME, LASTNAME and HW number.