Understanding horizontal shear in beam with vertical load

In summary, the image on the right is correct because it matches the statics. The image on the left is incorrect because it does not match the statics. The two images are consistent with two useful hints or guidelines from the author, but there is no explanation regarding either of my questions.
  • #1
davidwinth
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TL;DR Summary
I am trying to understand both why a horizontal shear is shown in the flange of a beam with a vertical load and how the directions are defined.
In an I-beam, the shear flow is usually shown drawn as on the left, not as drawn on the right. I do not understand why. I do understand:
  1. The total horizontal shear force must be zero, consistent with statics.This is satisfied in both images.
  2. The vertical direction matches the direction of the external load.
  3. There is a longitudinal horizontal shear (in to or out of the plane of the cross section). That, I understand.
My fundamental question is, Why is the image on the left correct and the image on the right incorrect, (or why do we say there is left/right shear at all)? Statics would also be satisfied with no left/right shear.

It matters because, when accounting for the direct shear due to an additional horizontal force (pushing to the right), we will subtract the shears on the upper right hand side of the left I-beam to get the net. If we were to use the right I-beam, we'd have to add the shears to get the net. So the net shear said to exist in the upper right flange of the I-beam depends vitally on the direction assigned to the shear flow, and yet I see no physical reason to favor of one or the other convention.

1. How can I understand why a vertical force produces horizontal (left/right) shear and
2. Why the direction is chosen as it is?

F15i8.png
 
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davidwinth said:
Thanks. That is one of the pages I looked at when trying to understand. The problem is that both beams I show are consistent with the "two useful hints" or "guidelines" the author lists. There is no explanation regarding either of my questions.
Keep in mind that this shear flow concept was developed for dealing with thin wall cross-sections.
I may be wrong, but this is the way in which I see it:

If you can visualize the flanges of the beam as thin plates, you can see that:
1) The difference of the shear forces in the y-direction are negligible.
2) Is the area of both plates that are connecting to the web the ones "feeling" the pulling and pushing of the axial forces induced by the moments.
3) The shear force next to the edges of a thin plate is close to zero in increase toward the central area of the plate, as the following link shows.

Please, see:
https://en.wikipedia.org/wiki/Bending_of_plates

Therefore, the arrows represent how the flow begins and the free edges of the top flange (just like it starts at the top edge of a rectangular cross-section loaded from the top), increases in magnitude until reaching a max at the neutral line of the beam, to decrease again until reaching the free edges of the bottom flange.
Note that the shear flow for a beam loaded by negative moment would be represented in the opposite direction.

Please, see:
https://mathalino.com/reviewer/mech...erials/relation-between-load-shear-and-moment

https://www.ae.msstate.edu/tupas/SA2/chA14.7_text.html
A14.7_ex1_figure5.gif
 
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Related to Understanding horizontal shear in beam with vertical load

1. What is horizontal shear in a beam with vertical load?

Horizontal shear in a beam with vertical load refers to the force that acts parallel to the cross-section of the beam, causing it to bend or deform. It is a result of the vertical load acting on the beam and is an important factor in understanding the structural integrity of the beam.

2. How is horizontal shear calculated in a beam?

Horizontal shear can be calculated by taking the summation of the forces acting on the beam in the horizontal direction. This includes the applied load, reactions at the supports, and any external forces acting on the beam.

3. What is the significance of understanding horizontal shear in a beam?

Understanding horizontal shear in a beam is crucial in determining the maximum load that the beam can withstand before it fails. It also helps in designing and constructing safe and stable structures.

4. How does horizontal shear affect the stability of a beam?

Horizontal shear can cause the beam to deflect or bend, which can lead to instability and failure if the shear force exceeds the beam's capacity. It is important to consider horizontal shear in the design and construction of beams to ensure their stability.

5. What are some common methods for reducing horizontal shear in beams?

Some common methods for reducing horizontal shear in beams include increasing the beam's depth, using thicker or stronger materials, adding support beams or columns, and incorporating shear reinforcement such as stirrups or shear studs.

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