TABLE 5 Forces in Truss Members (Fig. 46)
A, in^2 L, in U, kips S', kips
Member (cm^2 ) (mm) (kN) S,kips(kN) U^2 LIA SULIA (kN)AB 5 108 O +15.25 O O +15.25
(32.2) (2,743.2) (O) (+67.832) (O) (O) (+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 O +13.63 O O +13.63
(32.2) (2,743.2) (O) (+60.626) (O) (O) (+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 O -25.42 O O -25.42
(38.7) (4,572.0) (O) (-113.068) (O) (O) (-113.068)
BF 5 180 +1.00 O +36.0 O +1.97
(32.2) (4,572.0) (+4.448) (O) (+2,809.18) (O) (+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 O -32.71 O O -32.71
(38.7) (4,572.0) (O) (-145.494) (O) (O) (-145.494)
Total +135.5 -266.5
(+10,580.1) (-19,280.2)
- Calculate the force induced in each member solely
by the unit force
Calling the induced force U 9 produced solely by the unit tension in BF, record the results
in Table 5, considering tensile forces as positive and compressive forces as negative. - 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. - Evaluate the true force in the selected member
Use the relation BF = -\^SULI (AE)]I^V
2
Ll (AE)]. The numerator represents Aa; the de-
nominator represents A 4 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. - Evaluate the true force in each member
Use the relation S' = S + 1.97 U 9 where S' = true force. The results are shown in Table 5.