Page 37 - Handbook of Civil Engineering Calculations, Second Edition

1.20 STRUCTURAL STEEL ENGINEERING AND DESIGN

5. Solve the simultaneous equations in step 4 to evaluate the
forces in the truss members
A positive result in the solution signifies tension; a negative result, compression. Thus,
AB 3830-lb (17,036-N) compression; AC 2750-lb (12,232-N) compression; and AD
8080-lb (35,940-N) tension. To verify these results, it is necessary to select moment
axes yielding equations independent of those previously developed.
6. Resolve the reactions into their components
In Fig. 11b, show the reactions at the supports B, C, and D, each reaction being numeri-
cally equal to and collinear with the force in the member at that support. Resolve these re-
actions into their components.
7. Take moments about a selected axis
Take moments with respect to the axis through C parallel to the x axis. (Since the x com-
ponents of the forces are parallel to this axis, their moments are zero.) Then M Cx
10AB y 6AD y 10(0.894)(3830) 6(0.707)(8080) 0.
8. Take moments about another axis
Take moments with respect to the axis through D parallel to the x axis. So M Dx 4AB y
6AC y 4(0.894)(3830) 6(0.831)(2750) 0.
The computed results are thus substantiated.

ANALYSIS OF A COMPOUND SPACE TRUSS

The compound space truss in Fig. 12a has the dimensions shown in the orthographic pro-
jections, Fig. 12b and c. A load of 5000 lb (22,240 N), which lies in the xy plane and
makes an angle of 30° with the vertical, is applied at A. Determine the force induced in
each member, and verify the results.

Calculation Procedure:

1. Compute the true length of each truss member
Since the truss and load system are symmetric with respect to the xy plane, the internal
forces are also symmetric. As one component of an internal force becomes known, it will
be convenient to calculate the other components at once, as well as the total force.
Record in Table 4 the length of each member as projected on the coordinate axes. Cal-
culate the true length of each member, using geometric relations.
2. Resolve the applied load into its x and y components
Use only the absolute values of the forces. Thus P x 5000 sin 30° 2500 lb (11,120 N);
P y 5000 cos 30° 4330 lb (19,260 N).
3. Compute the horizontal reactions
Compute the horizontal reactions at D and at line CC
(Fig. 12b). Thus M CC
4330(12) 2500(7) 10H 1 0; H 1 3446 lb (15,328 N); H 2 3446 2500 946 lb
(4208 N).
4. Compute the vertical reactions
Consider the equilibrium of joint D and the entire truss when you are computing the verti-
cal reactions. In all instances, assume that an unknown internal force is tensile. Thus, at