# Drawing BMD & SFD for TRAPEZOIDAL LOAD on a beam with fixed supports

• Kelles
In summary, the person is a 3rd year civil engineering student who is struggling with drawing a shear force and bending moment diagram for a trapezoidal load on a beam with fixed supports. They know how to find support reactions but need an equation to find the maximum bending moment at mid-span. They are unsure if there are standard equations for trapezoidal loading or if they need to divide the beam into three sections and superimpose the diagrams. They have already developed a shear force diagram and believe the max bending moment occurs at mid-span. They are using a professional software called SAP2000 and the beam needs to be fixed at both ends. They are looking for a formula to find the maximum bending moment and have been advised
Kelles
I am a 3rd year civil engineering student and this is the first time i come across this problem and i am struggling with it.

My problem here is that i don't know how to draw a shear force and bending moment diagram for a trapezoidal load on a beam with fixed supports at both ends.

I know how to find the support reactions but i need an equation to find the maximum bending moment at mid-span.

Are there any standard equations to determine the different points on the Bending moment digram for trapezoidal loading or do i have to divide my beam into 3 section (1. left triangular loading, 2. UDL, 3. right triangular loading ) and then superimpose the resulting diagrams for the 3 sections.

I really need some help here...i have searched for hours online and i couldn't find anything for this.

I should have said that i am a 1st year i guess, anyways i think i have figured this out. i have separated the trapezoid into 3 sections and calculated the reactions for each one and then superimposed them. I think this works fine with the shear force diagram but i am unsure about the bending moment diagram since i have a beam with 2 different trapezoidal loadings on each side. Also i have another beam with a UDL one one side a trapezoidal on the other side.

Are you sure the beam is fixed at both ends (statically indeterminate to the 3rd degree) or is it pinned at both ends? Have you developed a shear diagram or have you just determined the end reactions? Does the max bending moment occur at mid point or elsewhere? To draw the bending moment diagram, the slope of the moment diagram at any point is equal to the value of the shear at that point. The moment reaches a maximum at a point of zero shear. Rather tedious for a trapezoidal load.

yes the beam is fixed at both ends...i am designing the beam, actually i am designing a whole steel frame structure with the aid of a professional software called SAP2000 and the joints need to be fixed because i am not using any vertical bracing.

I have already developed a shear force diagram by dividing the trapezoid into three sections and then superimposed the reactions.
If you could guide me on how to upload a picture i could show you the kind of trapezoidal loading i am talking about.

Yes the maximum bending moment is probably at mid-span, i haven't calculated it but from my experience i know its at midspan.

So my question now is about the BMD: If a calculate the bending moment that results at the supports and then multiply the shear force which i have calculated at 2 points between the beam with the distance from the support will i be able to draw a correct BMD?

I am looking for a formula to find the maximum bending moment for a trapezoidal loading, can anyone point me out to it?

You could refer to a book such as 'steel designers manual'.

## 1. What is a BMD and SFD?

BMD stands for "bending moment diagram" and SFD stands for "shear force diagram". These are graphical representations of the internal forces acting on a beam, typically used in structural engineering and mechanics to analyze and design structures.

## 2. How do you draw a BMD and SFD for a trapezoidal load on a beam?

To draw a BMD and SFD for a trapezoidal load on a beam, you will need to first calculate the magnitude and location of the internal forces at various points along the beam. This can be done using equations and principles of mechanics. Once you have the values, you can plot them on a graph, with the shear force on the vertical axis and the bending moment on the horizontal axis. A trapezoidal load will result in a triangular shape for the SFD and a parabolic shape for the BMD.

## 3. What do fixed supports mean in a beam?

Fixed supports, also known as fixed connections or fixed ends, refer to the points where a beam is supported and restrained from both translation and rotation. This means that the beam cannot move or rotate at these points, and any external load applied to the beam will cause internal forces to develop at these supports.

## 4. How do fixed supports affect the BMD and SFD for a trapezoidal load on a beam?

Fixed supports will have a significant impact on the BMD and SFD for a trapezoidal load on a beam. This is because the fixed supports will create additional internal forces in the beam, which will affect the magnitude and location of the forces shown in the diagrams. The fixed supports will also create "jump discontinuities" in the diagrams, where the values suddenly change due to the support's effect on the beam.

## 5. What are the key things to remember when drawing a BMD and SFD for a trapezoidal load on a beam with fixed supports?

When drawing a BMD and SFD for a trapezoidal load on a beam with fixed supports, it is important to remember to accurately calculate the internal forces at different points along the beam. You should also take into account the fixed supports and how they will affect the diagrams. Additionally, you should remember to label the axes and include a legend to explain what each line or shape represents. Finally, it is crucial to check your calculations and diagrams for accuracy to ensure that they accurately represent the behavior of the beam under the given load and support conditions.

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