Method of sections : As the name suggests in method of sections we make sections through a truss and then calculate the force in the members of the truss though which the cut is made. For example, if I take the problem we just solved in the method of joints and make a section S₁, S₂ (see figure 9), we will be able to determine the forces in members BC, BE and FE by considering the equilibrium of the portion to the left or the right of the section.

Let me now illustrate this. As in the method of joints, we start by first determining the reactions at the external support of the truss by considering it as a whole rigid body. In the present particular case, this gives N at D and N at A. Now let us consider the section of the truss on the left (see figure 10).

Since this entire section is in equilibrium, . Notice that we are now using all three equations for equilibrium since the forces in individual members are not concurrent. The direction of force in each member, one can pretty much guess by inspection. Thus the force in the section of members BE must be pointing down because there is no other member that can give a downward force to counterbalance N reaction at A. This clearly tells us that F BE is tensile. Similarly, to counter the torque about B generated by N force at A, the force on FE should also be from F to E. Thus this force is also tensile. If we next consider the balance of torque about A, N and F_FE do not give any torque about A. So to counter torque generated by F_BE , the force on BC must act towards B, thereby making the force compressive.

Let us now calculate individual forces. F_FE is easiest to calculate. For this we take the moment about B. This gives

4 × = 4 × F FE

F FE = N

Next we calculate F_BE . For this, we use the equation . It gives

Finally to calculate F_BC , we can use either the equation about A or

Thus we have determined forces in these three members directly without calculating forces going from one joint to another joint and have saved a lot of time and effort in the process. The forces on the right section will be opposite to those on the left sections at points through which the section is cut. This can be used to check our answer, and I leave it as an exercise for you.

After this illustration let me put down the steps that are taken to solve for forces in members of a truss by method of sections:

1. Make a cut to divide the truss into section, passing the cut through members where the force is needed.
2. Make the cut through three member of a truss because with three equilibrium equations viz. we can solve for a maximum of three forces.
3. Apply equilibrium conditions and solve for the desired forces.

In applying method of sections, ingenuity lies in making a proper. The method after a way of directly calculating desired force circumventing the hard work involved in applying the method of joints where one must solve for each joint.

We thus conclude one lecture or trusses. Next step in making the treatment accurate is obviously to take care of deformation in the members of a truss. This will be done in an advanced course later.