Page 84 - Handbook of Civil Engineering Calculations, Second Edition

STATICS, STRESS AND STRAIN, AND FLEXURAL ANALYSIS 1.67

TABLE 5. Forces in Truss Members (Fig. 46)
A, sq.in. L, in. U, kips S
, kips
2
2
Member (cm ) (mm) (kN) S, kips (kN) U L/A SUL/A (kN)
AB 5 108 0 15.25 0 0 15.25
(32.2) (2,743.2) (0) ( 67.832) (0) (0) ( 67.832)
BC 5 108 0.60 15.25 7.8 197.6 14.07
(32.2) (2,743.2) ( 2.668) ( 67.832) ( 615.54) ( 15,417.78) ( 62.588)
CD 5 108 0 13.63 0 0 13.63
(32.2) (2,743.2) (0) ( 60.626) (0) (0) ( 60.626)
EF 4 108 0.60 13.63 9.7 220.8 14.81
(25.8) (2,743.2) ( 2.688) ( 60.626) ( 756.84) ( 17,198.18) ( 65.874)
BE 4 144 0.80 4.50 23.0 129.6 2.92
(25.8) (3,657.6) ( 3.558) ( 20.016) ( 1,794.68) ( 10,096.24) ( 12.988)
CF 4 144 0.80 2.17 23.0 62.5 0.59
(25.8) (3,657.6) ( 3.558) ( 9.952) ( 1.794.68) ( 4,868.55) ( 2.624)
AE 6 180 0 25.42 0 0 25.42
(38.7) (4,572.0) (0) ( 113.068) (0) (0) ( 113.068)
BF 5 180 1.00 0 36.0 0 1.97
(32.2) (4,572.0) ( 4.448) (0) ( 2,809.18) (0) ( 8.762)
CE 5 180 1.00 2.71 36.0 97.6 0.74
(32.2) (4,572.0) ( 4.448) ( 9.652) ( 2,809.18) ( 6,095.82) ( 3.291)
DF 6 180 0 32.71 0 0 32.71
(38.7) (4,572.0) (0) ( 145.494) (0) (0) ( 145.494)
_________ _________
Total 135.5 266.5
( 10,580.1) ( 19,280.2)

3. Calculate the force induced in each member solely
by the unit force
Calling the induced force U, produced solely by the unit tension in BF, record the results
in Table 5, considering tensile forces as positive and compressive forces as negative.
4. Calculate the force induced in each member solely
by the applied loads
With BF eliminated, calculate the force S induced in each member solely by the applied
loads.
5. Evaluate the true force in the selected member
2
Use the relation BF [ SUL/(AE)]/[ U L/(AE)]. The numerator represents a ; the de-
nominator represents i for a 1-kip (4.45-kN) tensile force in BF. Since E is constant, it
cancels. Substituting the values in Table 5 gives BF ( 266.5/135.5) 1.97 kips
(8.76 kN). The positive result confirms the assumption that BF is tensile.
6. Evaluate the true force in each member
Use the relation S
S 1.97 U, where S
true force. The results are shown in Table 5.