EGR 220 Mechanics of Materials
Spring 2008
Homework Assignment # 10
Due : June 5 (Thursday)
This homework assignment introduces the concept of normal stress, shear stress,
and deflection of beam. ♣ Textbook problem : 6-23, 6-29(Beam Bending),
12-3, 12-26(Beam Deflection)
1. A bookshelf is made out of 6mm plate glass in Figure. For long-time service,
ordinary plate glass cannot safely be stressed to more than about 7MN/m2
in tension. If the supports are located in the optimum position, estimate the
average weight of books per unit length which can be placed along the shelf.
a
860 mm
6 mm
190 mm
a
2. A new theory of Egyptian pyramid-building proposes that the large pyramid
blocks were lifted onto sledges by the counterweighted wooden lever system
shown in Figure. The sledges were then pulled up the sides of the pyramid by
manpower. If the wood in the levers has an ultimate tensile stress of 52MN/m2
and ultimate shear stress of 10MN/m2 , find on the basis of these ultimate
stresses the dimensions of the smallest square piece of timber which will support
the pyramid blocks as shown.
1
4.5 m
b
1.8 m
b
26 kN
Counterweight
3. A rectangular beam on simple supports has bricks piled uniformly along its
length such that there is a total weight ωo of bricks per unit length along the
beam like Figure. Determine the ratio of the maximum bending stress σx to the
maximum shear stress τxy .
y
z
h
b
x
L
4. Two designs have been suggested for building a box beam by nailing together
four pieces of wood of equal thickness. The dimensions b and h and the spacing
s are equal in both designs like below figure. If the beam is to carry loading in
the xy plane, is one design better than the other?
y
y
s
s
h
h
z
z
x
b
x
b
5. In one of his discourses, Galileo tells a story about some Roman engineers
2
who had to transports a large stone column to the construction site of a new
temple. The standard method at that time was to place the column on two large
logs and draw it forward with oxen. However, previous experience with columns
of this size showed that they would break over one of the rollers. In order to
avoid this problem, the Romans added a third support. Galileo reports that the
column “broke upon the middle support”. Can you explain why?
b
h
A
Section A-A
A
L
4
L
2
L
4
L
2
L
2
L
2
3