Theory of Structures

Welcome, class! Today we will learn about the procedure for analyzing internal forces in beams. Can anyone tell me why we need to determine these forces?

We need to ensure the structural integrity of beams.

Exactly! Let’s start with the first step: computing support reactions. Remember the acronym SEEP: Support, External forces, Equilibrium, and Portion selection. Can anyone recall what we do in this step?

We apply equilibrium equations to find the support reactions on the beam, right?

Right! Now, in cantilever beams, we might skip this by analyzing the free portion instead. That’s a little trick to remember! Moving on, what’s the next step?

Cut the beam at the desired location.

Exactly! By passing a section where we want to analyze forces, we simplify the next calculations. Let’s look at how we select which beam portion to analyze next.

We look for the portion with fewer external forces.

Correct! This keeps our calculations simpler. Remember, simpler is better!

To summarize, first compute support reactions, cut the beam, and choose the portion. We'll cover the next steps next class.

Today we’ll discuss calculating the internal forces starting with axial force. Who can explain how we can do that?

We sum the external loads in the direction of the beam's axis.

Yes! The axial force is simply the sum of these forces. Let's remember 'ASAP' – 'Axial Sum Action'. Now, how about shear?

We add the components of forces perpendicular to the axis.

Exactly! We compute shear forces by summing perpendicular components. To summarize: Axial = Sum of parallel forces, Shear = Sum of perpendicular forces. Now, who would like to tackle bending moments?

That’s about taking moments around the section we cut, right?

Correct! Moments are calculated by summing the moments of external forces around that section. Make sure to grasp this as it’s essential for the next topic: verification.

How do we verify our calculations?

Good question! We can check our results using the other beam portion. If they're identical, our work is solid. Remember the formulae involved and stay engaged!

Now that we understand the theory, let’s apply this to real-world examples. Who would like to present their analysis of a beam?

I have a beam with a concentrated load. I found the support reactions first.

Great job! What did you find next?

I cut the beam at the load location to analyze axial force.

Did you find the shear force next?

Yes! I calculated the shear by summing the forces perpendicular to the axis.

Excellent! It's key to keep the order right: Axial, then Shear, then Bending Moment. Anyone else wants to share their process?

I used another example with a distributed load, and it was tricky!

Distributed loads can be complicated. Always look at applying the same steps systematically. Revisit each step and verify your work afterwards.

For homework, I want each of you to analyze a beam with a different load type and bring your steps to the next class.