**Question 1**

Question 2

Several forces (*F *= 200 N and *P *= 150 N) are applied to the pipe assembly as shown in Figure Q1(b). Knowing that the inner and outer diameters of the pipe are equal to 40 mm and 45 mm, respectively, determine:

a) the principal planes and the principal stresses at point H located at the top of the outside surface of the pipe and sketch the orientation of the element,

b) the maximum in-plane shearing stress at the same point and sketch the orientation of the element

c) the absolute maximum shearing stress at the same point

Question 3

An electrically heated process is known to exhibit

second-order dynamics with the following parameter val-

ues: K = 3 °C/kW, T = 3 min,~ = 0.7. If the process initially

is at steady state at 70 oc with heater input of 20 kW and

Exercises 89

the heater input is suddenly changed to 26 kW and held

there,

(a) What will be the expression for the process temperature

as a function of time?

(b) What will be the maximum temperature observed?

When will it occur?

Question 4

Answer to question 1

Answer to question 2

Given:

F = 200 N and P = 150 N

Outside diameter of the pipe, d_{o} = 45 mm

Inside diameter of the pipe, d_{i} = 40 mm

Solution: p

Two equal and opposite, non colinear forces of 200 N acting on the vertical pipe ED formed a twisting moment (M_{t}) due to which torsional shear stresses will be induced in the vertical sections of the horizontal pipe AC, while two equal and opposite non colinear forces of 150 N acting on the vertical pipe ED formed a bending moment (M_{b}) due to that bending stresses will be induced in the vertical sections of horizontal pipe AC. Thus point H is subjected to twisting moment as well as bending moment. So bending and shear stresses will be induced in the material of the pipe. The value of these stresses is calculated by applying torsion and bending equations. After that principal stresses and position of principal planes are calculated through Mohr circle method. Finally fin plane maximum shear stress and absolute maximum shear stress is calculated at point H.

Answer to question 3

Answer to question 4