Consider the "roll$-$formed" member shown in $($Figure $1).$ Suppose that a

$=42$ mm

$,$ b

$=160$ mm

$.$

Figure$1$ of $1$

A bent member consisting of five straight segments is shown in the x y plane. The x axis points horizontally to the right. The y axis points vertically upward. The member is symmetrical about the y axis. Two segments of length $\text{'}$a$\text{'}$ lie on the negative and positive x axis. One segment of length $\text{'}$a$\text{'}$ is parallel to the x axis with its midpoint on the positive y axis at distance b from the origin. Two segments of length b are parallel to the y axis and connect the ends of the horizontal members. The centroid of the member labeled C lies on the positive y axis at distance y bar from the origin.

Part A

Determine the location y$$

of the centroid C

of the "roll$-$formed" member. Neglect the thickness of the material and any slight bends at the corners.

Express your answer to three significant figures and include the appropriate units.

Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type

y$$

$=$

nothing