Question

Determine the forces in all the member of a cantilever truss shown in fig.

Answer 1

From triangle ACE, we have

Joint C:

Consider F_BD of joint C as shown in fig(a)

Since three forces are acting, so apply lami,s theorem at joint C.

T_BC/sin(90 – θ) = T_CD/sin 270 = 2000/sin θ

T_BC/cos θ = T_CD/sin 270 = 2000/sin θ

T_BC = 2000/tan θ = 2000/0.66 = 3000.3N ...(v)

T_BC = 3000.3N (Tensile)

T_CD = – 2000/sin θ = 2000/0.55 = 3604.9N ...(vi)

T_CD = 3604.9N (Compressive)

Joint B:

Consider FBD of joint B as shown in fig (b)

Since, T_BC = 3000.3N

Let, T_AB = Force in the member AB

T_DB = Force in the member DB

Since four forces are acting at joint B, So apply resolution of forces at joint B

RH = T_AB – T_BC = 0, T_AB = T_BC

= 3000.03 = T_AB

T_AB = 3000.03 ...(vii)

T_AB = 3000.03N (Tensile)

R_V = – T_DB – 2000 = 0

T_DB = -2000N ...(viii)

T_DB = 2000N (compressive)

Joint D: 

Consider FBD of joint D as shown in fig(c)

Since, T_DB = – 2000N

T_CD = 3604.9N

Let, T_AD = Force in the member AD

T_DE = Force in the member DE

Since four forces are acting at joint D, So apply resolution of forces at joint D.

R_V = 2000 + T_CD sin θ + T_AD sin θ – T_ED sin θ = 0

R_V = 2000 + T_CD sin θ + T_AD sin θ – T_ED sin θ = 0

T_AD – T_ED = 7241.26N ...(ix)

R_H = T_CD cos θ – T_AD cos θ – T_EDcos θ = 0

= 3604.9 = T_AD + T_ED

T_AD + T_ED = 3604.9 ...(x)

Solving equation (ix) and (x), we get

T_ED = 55423.1N ... (xi) 

T_ED = 5542.31N (Tensile) 

 T_AD = -1818.18N ...(xii) 

T_AD = 1818.18N (compressive)

Member	AB	BC	CD	DE	DB	AD
Force in N	3000.03	3000.03	3604.9	5542.31	2000	1818.18
Nature C = Compression T = Tension	T	T	C	T	C	C