Question

Determine the forces in the members BC and BD of a cantilever truss shown in the figure.

Answer 1

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 – T_BC 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 – T_BC x 1.5 = 0

T_BC = 1333.33KN ...(iii)

T_BC = 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

∑M_C = 0

{Moment of force T_AB, TC_D and 1000N acting at C is zero}

–1000 x BD – T_BD x BC = 0

–1000 x 2 – T_BD x 2 = 0

T_BD = – 1000KN...(iii)

TBC = 1000KN (compressive)