Shear Flow In Built Up Members

[Jake AA]

When calculating the shear flow at connections between two dissimilar materials (e.g. Wood beam with steel channel side by side), when would you apply the modular ratio?
I've seen examples two ways:
1) Simply divide it in the final shear flow equation q = (V*Q)/(I*n)
2) Use the modular ratio to transform your sections throughout the equations; EXAMPLE: Area of steel=A*n then you use the transformed area to calculate centroid. Then you use the modular ratio to find the Moment of Inertia using parallel axis theorem I = (I*n) + [(delta y^2)*A]. AND THEN you use the modular ratio again in the final equation q = (V*Q)/(I*n)

I'm confused when to use the modular ratio if anyone can help me out I'd really appreciate it.

 

[Smoulder]

The second way works. Not sure about the first way because you didn't give the full method. Doesn't work if it doesn't give same centroid and same Q as transformed area method.

 

[phamENG]

For a wood beam and channel side by side, I wouldn't be using shear flow. They'll share load based on stiffness - the bolts just ensure they deflect together along their length if the load isn't applied equally and to ensure the section won't buckle into separate pieces.

 

[canwesteng]

I would use the modular ratio throughout the process, else the centroid won't reflect the actual elastic centroid of the section. Think of a section under bending that is half wood and half steel, split horizontally about the plane of bending - if plane sections remain plane, and you have equal strains in the top and bottom fibers, due to the different stiffnesses you have different tension and compression forces and now the section is no longer under equilibrium for axial forces.

Like pham says, this doesn't seem like a shear flow problem and I wouldn't use wood as a composite member for steel anyway.

 

[rb1957]

the bolts are there to ensure the two deflect the same amount. I'm not sure the "rule of mixtures" (your option 2) does this "right".

I'd look at each beam separately. Apply 100 lbs to one, see what deflection do you get. Apply a load to the other to get the same deflection. But the loading of the two is different (unless there is a clip distributing the applied load to the two components). If there isn't then the load is applied to one component, and the fasteners transfer the load to the second. And the load transfer ensures the same deflection. Of course some may "fuss" that there is a slightly different deflection curve between the two components due to the shear deflection of the fasteners. This is of course true, but IMHO a second order effect

"Wir hoffen, dass dieses Mal alles gut gehen wird!"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.