Determining Ultimate Shear Stress in Glued Joints

In summary, the conversation is about determining the dimension X at which a glued joint will fail due to an ultimate shear stress of 1050 psi. The conversation includes equations for calculating shear stress and pressure, as well as a suggestion to sum moments about point A to solve for X. The PF rules for homework questions are also mentioned.
  • #1
williamx11373
21
0
http://s44.photobucket.com/albums/f46/maximus11373/?action=view&current=w-1.jpg&newest=1



An inclined member is braced with a glued block, as shown. The ultimate shear stress in the glued joint is 1050 psi. Determine the dimension X at which the glued joint will fail.


I know that


-shearstress= (Pressure x length) dived by (Area x modulus of elasticity)


- At point A there is X forces and Y forces, at point B there is Normal Force.


-Pressure max = (Shearstress X Area)


------------

so far i know that Force at A in the X direction is 1050x (2x2) = 4200 lbs



other than that I am stuck and i don't know where to start...any help would be appreciated.
 
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  • #2
williamx11373 said:
http://s44.photobucket.com/albums/f46/maximus11373/?action=view&current=w-1.jpg&newest=1



An inclined member is braced with a glued block, as shown. The ultimate shear stress in the glued joint is 1050 psi. Determine the dimension X at which the glued joint will fail.


I know that


-shearstress= (Pressure x length) dived by (Area x modulus of elasticity)
wrong equation
- At point A there is X forces and Y forces, at point B there is Normal Force.
yes, assuming the wall is frictionless
-Pressure max = (Shearstress X Area)
max average shear force = max shear stress x Area
------------

so far i know that Force at A in the X direction is 1050x (2x2) = 4200 lbs
Yes, good
other than that I am stuck and i don't know where to start...any help would be appreciated.
What must be the normal force on the ladder from the wall? Then try summing moments about A (must be equal to 0) to solve for X.
 
  • #3
Is there anyone out there that could help with this problem
 
  • #4
GreenwoodSpur: Someone did, above, in post 2. Regardless, the PF rules for homework questions state you must list relevant equations yourself, and show your work. And then someone might check your math. (See PF rules link at the top of each page.)
 
  • #5



As a scientist, it is important to approach this problem systematically and use appropriate equations and principles to determine the dimension X at which the glued joint will fail. First, it is necessary to understand the concept of shear stress and its relationship to force and area. Shear stress is a measure of the force per unit area that acts in a direction parallel to the surface of an object. In this case, the glued joint is experiencing a shear stress of 1050 psi, which means that for every square inch of the joint, there is a force of 1050 pounds acting parallel to the surface.

Next, we can use the equation for shear stress (τ = F/A) to determine the force acting on the glued joint. From the given information, we know that the force at point A in the X direction is 4200 lbs. Using this and the equation, we can calculate the area of the glued joint: A = F/τ = 4200 lbs / 1050 psi = 4 in^2.

Now, we can use the concept of equilibrium to determine the force at point B. Since the member is braced and the glued block is acting as a support, the force at point B must be equal in magnitude and opposite in direction to the force at point A. This means that the force at point B is also 4200 lbs in the X direction.

From here, we can use the equation for pressure (P = F/A) to calculate the pressure acting on the glued joint at point B. Since we know the force and the area (4 in^2) from earlier calculations, the pressure at point B is 4200 lbs / 4 in^2 = 1050 psi, which matches the given value for the ultimate shear stress in the glued joint.

Finally, to determine the dimension X at which the glued joint will fail, we can use the equation for pressure (P = F/A) again. This time, we will solve for the dimension X, which represents the length of the glued joint. Rearranging the equation, we get X = F/(P x A) = 4200 lbs / (1050 psi x 4 in^2) = 1 inch.

Therefore, the glued joint will fail when the dimension X of the glued joint is 1 inch. It is important to note that this calculation assumes ideal conditions and does not take into account factors such as material properties and joint design. As
 

1. What is the purpose of determining ultimate shear stress in glued joints?

The purpose of determining ultimate shear stress in glued joints is to understand the strength and stability of the joint under different loads. This information can help in selecting the appropriate glue and joint design for a given application, ensuring the safety and reliability of the joint.

2. How is ultimate shear stress in glued joints measured?

Ultimate shear stress in glued joints is typically measured through experiments, where a force is applied to the joint until it fails. The maximum force that the joint can withstand before failure is the ultimate shear stress.

3. What factors can affect the ultimate shear stress in glued joints?

The ultimate shear stress in glued joints can be affected by various factors such as the type of glue used, the quality of the bond surface, the type of wood or material being joined, and the design of the joint. The environmental conditions, such as temperature and humidity, can also have an impact on the ultimate shear stress.

4. What are some common methods for improving the ultimate shear stress in glued joints?

Some common methods for improving the ultimate shear stress in glued joints include using high-quality glue, properly preparing the bond surfaces, using appropriate clamping pressure and time, and selecting a suitable joint design. Additionally, using reinforcing materials or techniques such as dowels or splines can also increase the ultimate shear stress.

5. How does the ultimate shear stress of glued joints compare to other types of joints?

The ultimate shear stress of glued joints can vary depending on the factors mentioned above. In general, glued joints have a high ultimate shear stress compared to other types of joints, such as mechanical fasteners or welded joints. However, the specific strength of a joint will also depend on the specific materials and conditions involved.

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