Determine forces in members of cantilever truss:
Determine forces in members BC and BD of cantilever truss shown in the figure in the figure given below.
Sol.: If we draw a section line that cut the member BC, BD, AD, ED, then the member BC and BD cut by this line, but this section line cut 4 members, so we do not use this section line. As a section line cut maximum of three members.
There is no single section line that cut the maximum 3 member and also cut member BC and BD.
This problem can be solved in following two steps.
(1) Draw the section line which cut member BC and DC. Select any one section and find out value of BC.
(2) Draw the new diagram, draw another section line that cut the member AB, BD and CD, and find out value of the member BD.
STEP-1
Draw the section line which cut member BC and CD, as shown in figure given below.
Consider Right hand side of truss as shown in the figure given below
By taking moment about the point D
∑M_{D} = 0
1000 x 2 - T_{B}_{C} x BD = 0
Consider the ?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
T_{B}_{C} = 1333.33KN ...(iii)
T_{BC} = 1333.33KN (Tensile) .......ANS
STEP-2:
Draw the section line that cut the member AB, AD and BD, as shown in figure given below.
Consider the Right hand side portion of truss as shown in the figure given below
By taking moment about the point C
∑M_{C } = 0
{Moment of force T_{AB}, T_{C}_{D} and 1000N acting at point C is zero}
-1000 x BD - T_{B}_{D} x BC = 0
-1000 x 2 - T_{B}_{D} x 2 = 0
T_{B}_{D} = - 1000KN ...(iii)
T_{BC} = 1000KN (compressive) .......ANS