Mechanical Engineering Principles

BENDING MOMENT AND SHEAR FORCE DIAGRAMS 81

of the following simply supported beams;
hence, plot the bending moment and shearing
force diagrams.

1. Figure 6.41(a)
   [see Figure 6.44(a) on page 83)]

7 m

(a)

6 kN/m

AB

12 m

(b)

5 kN/m

AB

Figure 6.41 Simply supported beams

2. Figure 6.41(b)

[see Figure 6.44(b) on page 83)]

Determine expressions for the bending mo-
ment and shearing force distributions for each
of the following cantilevers; hence, or other-
wise, plot the bending moment and shearing
force diagrams.

3. Figure 6.42(a)

[see Figure 6.45(a) on page 83)]

5 m

(a)

6 kN/m

AB

9 m

(b)

5 kN/m

AB

Figure 6.42 Centilevers

4. Figure 6.42(b)

[see Figure 6.45(b) on page 83)]

Exercise 33 Short answer questions on

bending moment and shear-

ing force diagrams

1. Define a rigid-jointed framework


2. Define bending moment


3. Define sagging and hogging


4. State two practical examples of uniformly
   distributed loads


5. Show that the value of the maximum
   shearing force for a beam simply sup-
   ported at its ends, with a centrally placed
   load of 3 kN, is 1.5 kN.


6. If the beam in question 5 were of span
   4 m, show that its maximum bending
   moment is 3 kN m.


7. Show that the values of maximum bend-
   ing moment and shearing force for a can-
   tilever of length 4 m, loaded at its free
   end with a concentrated load of 3 kN, are
   12 kN m and 3 kN.

Exercise 34 Multiple-choice questions on

bending moment and shear-

ing force diagrams (Answers

on page 284)

1. A beam simply supported at its end, car-
   ries a centrally placed load of 4 kN. Its
   maximum shearing force is:
   (a) 4 kN (b) 2 kN (c) 8 kN (d) 0


2. Instead of the centrally placed load, the
   beam of question 1 has a uniformly dis-
   tributed load of 1 kN/m spread over its
   span of length 4 m. Its maximum shearing
   force is now:
   (a) 4 kN (b) 1 kN
   (c) 2 kN (d) 4 kN/n


3. A cantilever of length 3 m has a load
   of 4 kN placed on its free end. The mag-
   nitude of its maximum bending moment is:
   (a) 3 kN m (b) 4 kN m
   (c) 12 kN m (d) 4/3 kN/m
   Exercise 34 continued on page 83