Longitudinal shear in built-up beams
Longitudinal shear in built-up beams
(OP)
Hello all,
Hope everyone is well today. I am in the process of solving a conceptual question and I would appreciate everyone's input on this.
Please see the sketch attached. This is not the exact question I'm trying to solve but it is similar enough such that the concept can be carried over.
The goal is to find out the Longitudinal Shear at the connecting interface of the two beams shown and to figure out which weld size works best. I want to use the shear flow equation to compute the required shear force per unit length but I'm having some difficulty understanding how this equation is applied.
The equation is taken from a mechanics of materials text book. q=VQ/I; where q is the required shear (lb/ft), V is the shear force at the cross-section, Q is the moment of the area taken about the neutral axis, and I is the moment of intertia.
I have been able to calculate all the terms in equation except the 'Q' term based on this scenario. Any help would be greatly appreciated! Also, if there are any other methods to calculate the longitudinal shear at the connection interface of the two members, please feel free to share. :)
Hope everyone is well today. I am in the process of solving a conceptual question and I would appreciate everyone's input on this.
Please see the sketch attached. This is not the exact question I'm trying to solve but it is similar enough such that the concept can be carried over.
The goal is to find out the Longitudinal Shear at the connecting interface of the two beams shown and to figure out which weld size works best. I want to use the shear flow equation to compute the required shear force per unit length but I'm having some difficulty understanding how this equation is applied.
The equation is taken from a mechanics of materials text book. q=VQ/I; where q is the required shear (lb/ft), V is the shear force at the cross-section, Q is the moment of the area taken about the neutral axis, and I is the moment of intertia.
I have been able to calculate all the terms in equation except the 'Q' term based on this scenario. Any help would be greatly appreciated! Also, if there are any other methods to calculate the longitudinal shear at the connection interface of the two members, please feel free to share. :)






RE: Longitudinal shear in built-up beams
To calculate Q, draw a horizontal plane through the point where the welds occur. The area of the shape on one side of that plane has a centroid. Take the distance from that centroid of that area to the NA of the total shape. That is your d value. The area of the shape on one side of the plane is your A. Q = Ad.
RE: Longitudinal shear in built-up beams
RE: Longitudinal shear in built-up beams
If not, does this mean that we take the larger of the two 'Q' values?
RE: Longitudinal shear in built-up beams
2. You could calculate the flexural stresses at top and bottom of the existing W beam at a certain point in the span, say p1. Since the beam is symmetrical, the average stress in the beam is the average of those two values, say f1. You could do the same for another point, say p2 and find f2.
The axial force in the beam at p1 is A.f1. The axial force in the beam at p2 is A.f2. The difference is the force in the weld, Fw. If p1 and p2 are separated by distance L, the average force in the weld is Fw/L or A(f2-f1)/L.
3. You could calculate the flexural stress at the centroid of the Tee section at two points in the span, then determine the total force in the Tee at two points and repeat the same process as in 2. above.
This is, in fact how the VQ/I formula was derived. The change in axial force in a portion of the beam must be delivered by a horizontal shear in the weld.
BA
RE: Longitudinal shear in built-up beams
BA
RE: Longitudinal shear in built-up beams
RE: Longitudinal shear in built-up beams