What is a simply supported beam?
A simply supported beam rests on a support at each end and is free to bend in between. It is the simplest structural member there is, and almost every floor joist, bridge girder and shelf bracket is a version of it.
When a load is applied, the beam sags and its top surface shortens while its bottom surface lengthens. Those two effects are what engineers call tension and compression, and the stress they create is what decides whether the beam is strong enough.
Why tune the parameters?
The behaviour depends on four numbers: how big the load is, where along the span it sits, and how wide and how deep the cross-section is. Move any of them and the moment, the peak stress and the deflection all change.
Depth matters most. Because stiffness rises with the cube of the height, a deeper beam is dramatically stiffer, while making it wider helps only in proportion. Sliding the controls shows these trade-offs at once.
1. A point load is applied
A downward load P is placed on the span. Its position can be anywhere between the two supports, and the readouts follow it in real time.
2. The beam deflects
Under the load the beam sags into a smooth curve. The drawing exaggerates the deflection so a tiny real-world movement becomes visible.
3. The bending moment builds
Each support pushes back, creating a turning effect about every point in the beam. The moment rises from zero at the ends to a peak under the load, shown by the shaded triangle.
4. Stress appears across the section
The moment makes the section act like a lever. The top face is pushed into compression, the bottom face is pulled into tension, and the stress is greatest at those outer fibres.
5. The safety factor is compared
Dividing the steel's allowable stress by the peak stress gives the safety factor. Above one the beam survives the load; the higher the value, the more margin it has in reserve.
Where is the beam under the most stress?
The bending moment peaks directly under the point load, and the stress follows it. Slide the load towards mid-span and both the moment and the peak stress grow, because the lever arms on either side get longer.
What exactly is the bending moment?
It is the turning effect the load has about a cut through the beam. Multiply the load by the distance to each support and you get the moment, which is why the same load causes more bending near the middle of the span.
Why does the top face squash while the bottom stretches?
When a beam sags, it curves like a shallow rainbow. The top surface gets shorter and is pushed into compression, the bottom surface gets longer and is pulled into tension, and a neutral axis in between is left unstretched.
What does the safety factor mean?
It is the allowable stress of the steel divided by the stress the load actually causes. A value above one means the beam is safe; the higher the number, the more margin it has before it would start to yield.
Why does moving the load change the numbers?
The moment depends on the distances from the load to each support. Off-centre loads make one side short and the other long, and the product of those distances sets the peak moment and stress.
Why does a taller section bend less?
The section height enters the stiffness cubed, so doubling the height makes the beam about eight times stiffer, while a wider section only helps in proportion. Depth is the strongest lever on both stress and deflection.