Page 35 - Handbook of Civil Engineering Calculations, Second Edition

1.18 STRUCTURAL STEEL ENGINEERING AND DESIGN

2. Compute the resultant horizontal
soil thrust
Compute the resultant horizontal thrust T lb of
the soil by applying the coefficient of active
earth pressure. Determine the location of T.
Thus BG 0.333(15)(100) 500 lb/lin ft
(7295 N/m); T 0.5(15)(500) 3750 lb
(16,680 N); y 0.333(15) 5 ft (1.5 m).
3. Compute the maximum frictional
force preventing sliding
The maximum frictional force F m ( W),
where coefficient of friction. Or F m
0.6(11,625) 6975 lb (31,024.8 N).
4. Determine the factor of safety
against sliding
The factor of safety against sliding is FSS
F m /T 6975/3750 1.86.
5. Compute the moment of the
FIGURE 10 overturning and stabilizing forces
Taking moments with respect to C, we find the
overturning moment 3750(5) 18,750 lb·ft
(25,406.3 N·m). Likewise, the stabilizing mo-
ment 2250(0.5) 5625(2.67) 3750(4.33)
32,375 lb·ft (43,868.1 N·m).
6. Compute the factor of safety against overturning
The factor of safety against overturning is FSO stabilizing moment, lb·ft (N·m)/over-
turning moment, lb·ft (N·m) 32,375/18,750 1.73.

ANALYSIS OF A SIMPLE SPACE TRUSS

In the space truss shown in Fig. 11a, A lies in the xy plane, B and C lie on the z axis, and
D lies on the x axis. A horizontal load of 4000 lb (17,792 N) lying in the xy plane is ap-
plied at A. Determine the force induced in each member by applying the method of joints,
and verify the results by taking moments with respect to convenient axes.

Calculation Procedure:

1. Determine the projected length of members
Let d x , d y , and d z denote the length of a member as projected on the x, y, and x axes, re-
spectively. Record in Table 3 the projected lengths of each member. Record the remain-
ing values as they are obtained.
2. Compute the true length of each member
2
2
2 0.5
Use the equation d (d x d y d z ) , where d the true length of a member.
3. Compute the ratio of the projected length to the true length
For each member, compute the ratios of the three projected lengths to the true length. For
example, for member AC, d z /d 6/12.04 0.498.