Calculating the safe load of a glued structure with given shear stress

In summary, the maximum shear stress applies at the location y=0 on the beam. The shear stress provided is for the glued joints at y = 1cm, so the equation for maximum shear stress can be used to calculate the safe load for this location.
  • #1
maitake91
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Homework Statement
A laminated wood beam made up of three 2cm*4cm plates glued together forming a rectangular cross section that is 4cm*6cm is given. The allowable shear stress in the glued joints is 5MPa. The beam is 10cm long and simply supported at both ends.
What is the safe load that can be carried at mid-span and what is the corresponding. maximum bending stress?
Relevant Equations
maximum shear stress in a rectangular beam = 1.5(F/A)
I have tried to calculate the safe load with the equation of maximum shear stress, A = 4*6*10^-4, and the given shear stress 5MPa, but I couldn't seem to get the right answer which is 18kN.
 

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  • #2
Quote
maximum shear stress in a rectangular beam = 1.5(F/A)

To where on the beam does the maximum shear stress apply?
 
  • #3
Thank you for your reply!

I think it is at x=0 and x=l, therefore the value F I obtain from the equation is P_max/2?
In that case I'm getting 5*10^6*(4*6*10^-4)*(2/3) = 8000, which is not 9000 as the given answer suggests and I don't know why.
 
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  • #4
maitake91 said:
Thank you for your reply!

I think it is at x=0 and x=l, therefore the value F I obtain from the equation is P_max/2?
In that case I'm getting 5*10^6*(4*6*10^-4)*(2/3) = 8000, which is not 9000 as the given answer suggests and I don't know why.
For your beam and the related moment and shear force diagrams, shear force acts along the whole beam from 0 to L, with the shear force changing direction at the point of application of the load point P in the centre of the beam.

A shear stress is set up on a face of cross section of the beam in the y-direction. Correspondingly, to make the beam statically in equilibrium, also in the x-direction. For a location y from the central axis, a cube of dimensions dx dy dz would have shear on both opposite faces being equal in magnitude.

For your beam, on this face of cross section, where does the maximum shear stress apply?
 
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  • #5
256bits said:
For your beam and the related moment and shear force diagrams, shear force acts along the whole beam from 0 to L, with the shear force changing direction at the point of application of the load point P in the centre of the beam.

A shear stress is set up on a face of cross section of the beam in the y-direction. Correspondingly, to make the beam statically in equilibrium, also in the x-direction. For a location y from the central axis, a cube of dimensions dx dy dz would have shear on both opposite faces being equal in magnitude.

For your beam, on this face of cross section, where does the maximum shear stress apply?
Thank you very much, I was able to get the correct answer!

I finally realised that the maximum shear stress applies at y=0, but the shear stress provided is for the glued joints at y = 1cm, therefore I can't just use the equation for maximum shear stress.
 
  • #6
Let's see your complete analysis of the beam.
 

1. How is shear stress calculated for a glued structure?

Shear stress is calculated by dividing the force applied to the structure by the cross-sectional area of the glued joint. This will give you the shear stress in units of force per unit area, such as pounds per square inch (psi).

2. What is the safe load for a glued structure with a given shear stress?

The safe load for a glued structure with a given shear stress can be calculated by dividing the maximum shear stress that the glue can withstand by the calculated shear stress for the structure. This will give you the maximum load that the structure can safely bear without failure.

3. How do different types of glue affect the safe load of a structure?

Different types of glue have different shear strength values, which can affect the safe load of a structure. For example, a stronger glue will be able to withstand higher shear stress, resulting in a higher safe load for the structure. It is important to choose the appropriate type of glue for the specific application to ensure the safety and stability of the structure.

4. What other factors besides shear stress should be considered when calculating the safe load of a glued structure?

In addition to shear stress, other factors that should be considered when calculating the safe load of a glued structure include the type and quality of the materials being used, the design and construction of the structure, and any external forces that may be applied to the structure.

5. Can the safe load of a glued structure change over time?

Yes, the safe load of a glued structure can change over time due to factors such as environmental conditions, aging of the materials, and wear and tear on the structure. It is important to regularly inspect and maintain glued structures to ensure their safety and stability over time.

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