Page 25 - Handbook of Civil Engineering Calculations, Second Edition

1.8 STRUCTURAL STEEL ENGINEERING AND DESIGN

5. Verify the computed result
Draw a free-body diagram of member BC, and take moments with respect to C. The result
verifies that computed above.

GRAPHICAL ANALYSIS OF A PLANE TRUSS

Apply a graphical analysis to the cantilever truss in Fig. 4a to evaluate the forces induced
in the truss members.

Calculation Procedure:

1. Label the truss for analysis
Divide the space around the truss into regions bounded by the action lines of the external
and internal forces. Assign an uppercase letter to each region (Fig. 4).
2. Determine the reaction force
Take moments with respect to joint 8 (Fig. 4) to determine the horizontal component of
the reaction force R U . Then compute R U . Thus M 8 l2R UH 3(8 16 24) 5(6
12 18) 0, so R UH 27 kips (120.1 kN) to the right.
12
Since R U is collinear with the force DE, R UV /R UH / 24, so R UV 13.5 kips (60.0 kN)
upward, and R U 30.2 kips (134.3 kN).
3. Apply the equations of equilibrium
Use the equations of equilibrium to find R L . Thus R LH 27 kips (120.1 kN) to the left,
R LV 10.5 kips (46.7 kN) upward, and R L 29.0 kips (129.0 kN).
4. Construct the force polygon
Draw the force polygon in Fig. 4b by using a suitable scale and drawing vector fg to rep-
resent force FG. Next, draw vector gh to represent force GH, and so forth. Omit the ar-
rowheads on the vectors.
5. Determine the forces in the truss members
Starting at joint 1, Fig. 4b, draw a line through a in the force polygon parallel to member
AJ in the truss, and one through h parallel to member HJ. Designate the point of intersec-
tion of these lines as j. Now, vector aj represents the force in AJ, and vector hj represents
the force in HJ.
6. Analyze the next joint in the truss
Proceed to joint 2, where there are now only two unknown forces—BK and JK. Draw a
line through b in the force polygon parallel to BK and one through j parallel to JK. Desig-
nate the point of intersection as k. The forces BK and JK are thus determined.
7. Analyze the remaining joints
Proceed to joints 3, 4, 5, and 6, in that order, and complete the force polygon by continu-
ing the process. If the construction is accurately performed, the vector pe will parallel the
member PE in the truss.
8. Determine the magnitude of the internal forces
Scale the vector lengths to obtain the magnitude of the internal forces. Tabulate the results
as in Table 1.
9. Establish the character of the internal forces
To determine whether an internal force is one of tension or compression, proceed in this
way: Select a particular joint and proceed around the joint in a clockwise direction, listing