In this problem; If we draw a section line which cut the member BC, BD, AD, ED, then the member BC and BD cut by this line, but this section line cut four members, so we don’t use this section line. Since a section line cut maximum three members.
There is no single section line which cut the maximum three member and also cut the member BC and BD. This problem is done in two steps
(1) Draw a section line which cut the member BC and DC. Select any one section and find the value of BC.
(2) Draw a new diagram, draw another section line which cut the member AB, BD and CD, and find the value of the member BD.
STEP–1
Draw a section line which cut the member BC and CD, as shown in fig(a)
Consider Right hand side portion of the truss as shown in
Taking moment about point D
∑MD = 0
1000 x 2 – TBC x BD = 0
Consider Triangle CAE and CDB, they are similar
BD/AE = BC/AC
BD/3 = 2/4
BD = 1.5m
1000 x 2 – TBC x 1.5 = 0
TBC = 1333.33KN ...(iii)
TBC = 1333.33KN (Tensile)
STEP–2:
Draw a section line which cut the member AB, AD and BD, as shown in fig(b)
Consider Right hand side portion of the truss as shown in fig(c) Taking moment about point C
∑MC = 0
{Moment of force TAB, TCD and 1000N acting at C is zero}
–1000 x BD – TBD x BC = 0
–1000 x 2 – TBD x 2 = 0
TBD = – 1000KN...(iii)
TBC = 1000KN (compressive)
