A timber specimen of 40.33 mm width,70.07 mm depth and 604mm length and its weight is 798.9g carried loads(kN):
4,6,8,10,12,14,16,18,20,22,24,25.7.
and deflection(mm)
0.44,0.87,1.34,1.81,2.29,2.79,
3.39,4.17,5.42,7.21,11.02,21.94
please,
1-find density of timber.
2-determine maximum load that can be taken before deflection become or the failure if the failure occurs before maximum deflection is reached.
3. calculate the failure stress and young modulus for beam
To answer your questions, we will need to use some equations and formulas related to the properties of the timber specimen.
1. Finding the density of timber:
Density is calculated by dividing the weight of an object by its volume.
Density = Weight / Volume
In this case, the weight of the timber is given as 798.9g. To calculate the volume, we need the dimensions of the timber specimen, specifically its width, depth, and length.
Volume = Width x Depth x Length
Substituting the given values:
Volume = 40.33mm x 70.07mm x 604mm
Now, convert the volume to the same unit as weight (grams) to ensure consistent units.
Density = Weight / Volume
2. Determining the maximum load before failure:
To determine the maximum load before failure, we need to analyze the relationship between the applied load and the deflection of the beam. By examining the provided deflection values, we can identify the load at which the deflection exceeds the maximum allowed deflection.
3. Calculating the failure stress and Young's modulus:
To calculate the failure stress, we need to know the maximum load at failure. Once we know the maximum load, we can calculate the failure stress using the formula:
Failure Stress = Maximum Load / Cross-sectional Area
The cross-sectional area of the timber beam can be found using the width and depth values.
Young's modulus describes the stiffness of the material and is calculated using the formula:
Young's Modulus = Stress / Strain
Here, stress can be calculated as the maximum load divided by the cross-sectional area, and strain can be calculated as the maximum deflection divided by the length of the beam.
By substituting the values obtained, we can calculate the failure stress and Young's modulus for the timber beam.
Keep in mind that to accurately calculate these values, it's important to make sure the units of all measurements are consistent (e.g., converting millimeters to the same unit as weight, such as grams).