Mechanical Engineering Principles

102 MECHANICAL ENGINEERING PRINCIPLES

Assignment 2

This assignment covers the material

contained in Chapters 5 to 7.

The marks for each question are shown

in brackets at the end of each question.

1. A moment of 18 N m is required to oper-
   ate a lifting jack. Determine the effec-
   tive length of the handle of the jack (in
   millimetres) if the force applied to it is
   (a) 90 N (b) 0.36 kN (6)


2. For the centrally supported uniform beam
   shown in Figure A2.1, determine the val-
   ues of forcesF 1 andF 2 when the beam
   is in equilibrium. (7)

2 m 5 m

R= 5.6 kN

F 1 F 2

Figure A2.1

3. For the beam shown in Figure A2.2 cal-
   culate (a) the force acting on supportQ,
   (b) distanced, neglecting any forces aris-
   ing from the mass of the beam. (7)

5 N 20 N 10 N

= 15 N

1 m

3 m

6 m

9 m

d

P Q

RP R

Q

Figure A2.2

4. A beam of length 3 m is simply sup-
   ported at its ends. If a clockwise couple
   of 4 kN m is placed at a distance of 1 m
   from the left hand support, determine the
   end reactions. (4)


5. If the beam in question 4 carries an addi-
   tional downward load of 12 kN at a dis-
   tance of 1 m from the right hand support,
   sketch the bending moment and shearing
   force diagrams. (5)


6. A beam of length 4 m is simply supported
   at its right extremity and at 1 m from the
   left extremity. If the beam is loaded with a
   downward load of 2 kN at its left extrem-
   ity and with another downward load of
   10 kN at a distance of 1 m from its right
   extremity, sketch its bending moment and
   shearing force diagrams. (6)


7. (a) Find the second moment of area and
   radius of gyration about the axis
   XXfor the beam section shown in
   Figure A2.3.

6.0 cm

2.0 cm

2.0 cm

8.0 cm

10.0 cm

1.0 cm

XX

Figure A2.3

(b) Determine the position of the cen-

troid of the section.

(c) Calculate the second moment of area

and radius of gyration about an axis

through the centroid parallel to axis

XX. (25)