What is the difference between bending moment and moment of resistance?

To understand this difference, one must know the difference between ‘Analysis’ and ‘Design’.

Analysis is deterministic. We know what we need to do. For instance, if we are given a

simply supported beam with some loads acting on it and are asked to find out the maximum bending moment, we know exactly what to do.

If both of us solve the same problem we will get the same unique answer. We did not need the information regarding anything else. We didn’t bother what material the beam was made of.

We made an inherent assumption that whatever it is made of, is strong enough to take the bending moment that we calculated.

This assumption of ignoring the material to find out the bending moment makes sense because of the following reason.

We are not judging or assessing the beam (or any structure) when we talk about bending moments. Bending moments only tell us what the loads are like. You could say it is synonymous to a net load that a section in the beam feels.

Now, design is not deterministic. If you and I are asked to design this particular beam using a material like, say concrete, we may not come up with the same answer. Regardless, both can be right. This has to do with the moment of resistance.

This is where the material information comes into picture. Any beam (or column) resists the bending moment by forming a force couple at all sections along the length. A beam that is bending will develop equal and opposite forces at the two ends (top and bottom) of its cross section. The forces are tensile on one side of the neutral axis while they are compressive on the other side. Resultant of these forces are some distance apart from each other (lever arm) and they form a couple.

This force (both forces are equal, so pick one) multiplied by the lever arm gives a moment. While bending, the beam makes sure that this moment is always rotating in the opposite direction as the applied bending moment, to resist it.

We say that the beam doesn’t fail if the maximum moment of resistance (which can be calculated if we know the section properties-material and geometry) is greater that the maximum applied bending moment (calculated with load and global geometry information).

This is why in design, two of us may get different results because the condition only says that the resistance has to be greater. I could design it to be 10% greater while you could do 15%. Our beams will look different

With RK MAURYA

To understand this difference, one must know the difference between ‘Analysis’ and ‘Design’.

Analysis is deterministic. We know what we need to do. For instance, if we are given a

simply supported beam with some loads acting on it and are asked to find out the maximum bending moment, we know exactly what to do.

If both of us solve the same problem we will get the same unique answer. We did not need the information regarding anything else. We didn’t bother what material the beam was made of.

We made an inherent assumption that whatever it is made of, is strong enough to take the bending moment that we calculated.

This assumption of ignoring the material to find out the bending moment makes sense because of the following reason.

We are not judging or assessing the beam (or any structure) when we talk about bending moments. Bending moments only tell us what the loads are like. You could say it is synonymous to a net load that a section in the beam feels.

Now, design is not deterministic. If you and I are asked to design this particular beam using a material like, say concrete, we may not come up with the same answer. Regardless, both can be right. This has to do with the moment of resistance.

This is where the material information comes into picture. Any beam (or column) resists the bending moment by forming a force couple at all sections along the length. A beam that is bending will develop equal and opposite forces at the two ends (top and bottom) of its cross section. The forces are tensile on one side of the neutral axis while they are compressive on the other side. Resultant of these forces are some distance apart from each other (lever arm) and they form a couple.

This force (both forces are equal, so pick one) multiplied by the lever arm gives a moment. While bending, the beam makes sure that this moment is always rotating in the opposite direction as the applied bending moment, to resist it.

We say that the beam doesn’t fail if the maximum moment of resistance (which can be calculated if we know the section properties-material and geometry) is greater that the maximum applied bending moment (calculated with load and global geometry information).

This is why in design, two of us may get different results because the condition only says that the resistance has to be greater. I could design it to be 10% greater while you could do 15%. Our beams will look different

With RK MAURYA

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