Test: Method of Section - Mechanical Engineering MCQ

Take the section X-X and consider the upper part of the section. 

Take moment about C
F_DF x 4 + 2 x 3 = 0
F_DF x 4 = - 2 x 3
⇒ F_DF = - 1.5 kN = 1.5 kN (Compression) 

T₁ cos30 + T₂ cos60 = F
0.866 T₁ + 0.5 T₂ = F  ......(1)
T₁ sin 30° = T₂ sin60°
T₁ = 1.732 T₂   ......(2)​
From (1) and (2):
2T₂ = F ⇒ T₂ = F/2 = 2/2 = 1 kN
T₁ = 1.732 kN
R_B = T₂ sin60 = 0.866 kN
R_A = T₁ sin30 = 0.866 kN

Form force and moment equilibrium:
G_x = P, G_y = 0, H_x = 0
To calculate the fore in member DF, take joint D or F. know the forces in any member
Looking at joint A:

looking at joint B:

looking at joint D

Looking at joint G:

At point P,

Using Lami’s theorem

Now, again from equation (1)

At point S,


F_PS × cos θ = F_SQ × cos θ
F_PS = F_SQ = 11.25 kN
F_SQ = 11.25 kN (tensile)
As both F_PS and F_SQ have opposite directions.

Method of section cuts the whole structure of trusses into a section and then uses the cut out portion for the calculations of the unknown forces. For this method, we don’t require two forces to be collinear. But if the forces are collinear than the task of determining the unknown forces is very easy.

Method of joints defines as if the whole truss is in equilibrium then all the joints which are connected to that truss is in equilibrium. While the method of section cuts the whole structure of trusses into section and then uses the cut out portion for the calculations of the unknown forces. Thus both the methods are used for the same purpose.

The determination of the force of the unknown element is done by the method of section. For this the section is isolated from the main structure and then calculation is done after. But before that the determination of the support reaction needs to be done.

The determination of the force of the unknown element is done by the method of the section. For this the section is isolated from the main structure and then the calculation is done after. But before that the determination of the support reaction needs to be done.

The main methods for the solving for the unknown force on the truss are method of section and the method of joints. The other method is just given for the sake of confusion. This means that only two main methods are to applied for solving the unknown force on a truss.

The part of the calculation is made easier if the flow diagram of that section is made which is having the least number of forces. Thus for the sake of the calculation this is done. Or one can say that for getting the unknown force we use this method.