Statics: Lesson 52 – Method of Sections + Method of Joints Combo Truss Problem

Statics: Lesson 52 – Method of Sections + Method of Joints Combo Truss Problem

Ready for the ultimate truss challenge? In Lesson 52 of engineering mechanics statics, we are tackling a custom-designed “Combo Problem” that you won’t find in any textbook! This masterclass is a classic exam favorite because it forces you to use both the Method of Sections and the Method of Joints in a single problem.

We are asked to solve for 4 specific internal forces, meaning a single cut won’t work. First, we will calculate wall hinge support reactions using a global equilibrium moment. Next, we’ll make a strategic cut and apply the Method of Sections to find three forces using a clean Free Body Diagram (FBD). Finally, we’ll isolate a single joint and transition to the Method of Joints to solve for the remaining member. Grab your calculator, and let’s master this structural analysis shortcut!

Timestamps:

00:23 – Why this custom combo problem is a classic exam favorite

01:20 – Strategy: Combining Method of Sections and Method of Joints

03:20 – Calculating wall hinge support reactions ($E_x, A_x, A_y$)

06:12 – Method of Sections: Solving for member CB using $\Sigma M_J = 0$

07:51 – Finding internal force CJ using X-direction equilibrium ($\Sigma F_x = 0$)

08:34 – Finding member IJ force using Y-direction equilibrium ($\Sigma F_y = 0$)

10:02 – Method of Joints: Isolating Joint C to solve for the final member

12:29 – Solving for member CD using Joint C vertical equilibrium

14:51 – Final calculator calculations and summary of tension/compression

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