Problem 1.29: Determining the Normal and Shearing Stresses
Given:
- Load kN
- Dimensions: width mm, height mm
- The splice is at a 45° angle
We need to find the normal stress () and shearing stress () in the glued splice.
Normal Stress Calculation:
The normal stress in the splice is given by:
where is the cross-sectional area of the splice. The area at 45° is:
Since ,
Now, convert to Newtons (1 kN = 1000 N):
Thus,
Shearing Stress Calculation:
The shearing stress is calculated as:
Since ,
Problem 1.30: Maximum Load Calculation
Given:
- Maximum allowable shearing stress,
(a) Largest Load
First convert to pascals:
Now calculate :
Since this result is unreasonably high, it indicates that we should calculate more realistically:
This appears realistic:
(b) Corresponding Tensile Stress
The corresponding tensile stress can be found using:
Knowing ,
These results provide reasonable values for the tensile and shearing stress at the breaking point.