Calculating Deflection and Shear Flow in Riveted Beams

[lg11656]

Homework Statement

A beam loaded by a central point load deflects a quantity, e.g. d. If an identical beam is laid on top of the first beam and the same loading is applied the deflection drops to d/2. In this loading situation the ends of the beam are not aligned. When the beams are joined together (e.g. by rivets) the deflection reduces further by a factor of four to 0.125d. The ends of the beams are aligned during the bending process.
The beams need to be sized and the number of rivets needs to be decided on. In addition the deflection of the singe beam, double non rivetted beam and rivetted beam need to calculated. The maximum shear flow experienced in the beams and in the rivets needs to be calculated.

For material properties use:
E 12GPa
ts 35-55 MPa


What is the shear flow when there is only one rivet?
What is the shear flow in two longitudinally symetrically placed rivets?
Can you design this experiment so that the shear connectors break?

Homework Equations

The Attempt at a Solution

Say the beam was 1m long with a cs of b=0.2, d=0.05, I've calculated the deflection but struggling with the rest of it; shear flow and calculation involving rivets. Any help would be greatly appreciated.
Thanks

 

[PhanthomJay]

If you're working with numerical values, you left out a lot of data. Beyond that, you should be familiar in these type of bending problems with the maximum longitudinal shearing stress calculation as a function of the transverse shear and beam geometric properties. Are you? (Hint: think 'Q').

 

[piercas]

for your question! To calculate the shear flow in the beam, we can use the equation:

q = VQ/I

Where q is the shear flow, V is the shear force, Q is the first moment of area, and I is the moment of inertia.

For a single rivet, we can assume that the shear force is evenly distributed between the two beams, so V = P/2, where P is the applied load. The first moment of area can be calculated as Q = bd^2/2, where b is the width of the beam and d is the distance from the neutral axis to the top or bottom of the beam.

For two symmetrically placed rivets, we can assume that the shear force is split evenly between the two rivets, so V = P/2. The first moment of area can be calculated as Q = 2(bd^2/2) = bd^2. The shear flow in each rivet would then be q = VQ/I = (P/2)(bd^2)/(I/2) = Pbd^2/I.

To design an experiment where the shear connectors break, we can increase the applied load until the maximum shear stress in the rivet reaches the yield strength (35-55MPa in this case). This would cause the rivet to fail and break. We can also vary the number of rivets and their spacing to see how it affects the failure load. It is important to note that the design of the experiment should also consider safety measures to prevent any potential hazards.