How to determine the principal stresses when you are not given the angle, but you have the bending stress and shear stress.

To determine the principal stresses when you are not given the angle, but you have the bending stress and shear stress, you can use the following steps:

1. Calculate the normal stress at a specific point using the bending stress formula:
σ = M*y/I
where:
σ = normal stress
M = bending moment
y = distance from the neutral axis to the point of interest
I = moment of inertia

2. Calculate the resultant stress at the same point by adding the normal stress and the shear stress:
σ_resultant = √(σ^2 + τ^2)
where:
σ_resultant = resultant stress
σ = normal stress
τ = shear stress

3. Repeat steps 1 and 2 for different points along the material to determine the maximum and minimum resultant stresses.

4. The maximum and minimum resultant stresses represent the principal stresses at that point.

By following these steps, you can determine the principal stresses when you are not given the angle but have the bending stress and shear stress.

Step 1: Identify the Given Values

- Bending stress (σ_b)
- Shear stress (τ_xy)

Step 2: Calculate the Maximum Principal Stress (σ_1)

```
σ_1 = (σ_b^2 + 3τ_xy^2) / (2σ_b)
```

Step 3: Calculate the Minimum Principal Stress (σ_3)

```
σ_3 = (σ_b^2 + 3τ_xy^2) / (2σ_b) - σ_b
```