## Cross Bar

In the below diagram, a cross plane member has a 15 mm uniform thickness and some loads in compression/tension. What is the max shear stress at the origin?

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__**Hint**

**Hint**

Stress:

$$$\sigma = \frac{Load}{Area}$$$

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__**Hint 2**

**Hint 2**

The max shear stress considering three dimensions:

$$$\tau_{max}=\frac{\sigma_y-\sigma_x}{2}$$$

The stress at the origin can be represented as:

which looks like a typical Mohr's Circle problem. To construct a Mohr's circle, the following sign conventions are used:

Since
$$stress=\frac{load}{area}$$

$$$\sigma_x=\frac{4,000N}{(0.05m)(0.015m)}=-5.33\:MPa$$$

$$$\sigma_y=\frac{2,000N}{(0.05m)(0.015m)}=2.67\:MPa$$$

Since
$$\sigma_x$$
is compressive:

$$$\sigma_1=2.67\:MPa$$$

$$$\sigma_2=0\:MPa$$$

$$$\sigma_3=-5.33\:MPa$$$

The max shear stress considering three dimensions is always:

$$$\tau_{max}=\frac{\sigma_1-\sigma_3}{2}=\frac{2.67-(-5.33)}{2}=4\:MPa$$$

4 MPa