Please solve a$,$ b$,$ and c $.$

Learning Goal:

To analyze two built$-$up members that have the same geometry but are fastened differently, determine the maximum applicable shear force on each cross section, and determine the adjustment in spacing between the weaker member$$s fasteners that would allow the member to support the equivalent maximum shear force of the stronger member.

The two cross sections shown below, $($a$)$ and $($b$),$ are subjected to a vertical shear force as shown. The members are fastened by nails that can support a load of $21\mathrm{.}00$ kN each and are spaced perpendicularly to the page in increments of s $=125\mathrm{.}0$ mm $.$ The geometries of the cross sections are given by a $=225\mathrm{.}0$ mm $,$ b $=50\mathrm{.}00$ mm $,$ c $=260\mathrm{.}0$ mm $,$ d $=125$ mm $,$ and e $=310$ mm $.$ Assume the cross sections are uniform along the entire lengths of the members.

Part A $-$ Maximum applicable shear force on the member $($a$)$

Determine the maximum applicable shear force on the member $($a$).$

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

Part B $-$ Maximum applicable shear force on the member $($b$)$

Determine the maximum applicable shear force on the member $($b$).$

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

Part C $-$ Spacing adjustment to the weaker member for equivalent maximum applicable shear force

Determine the required spacing in the weaker member such that both cross sections can support the same maximum applicable shear force as defined by the stronger member.

Express your answer to four significant figures and include the appropriate units. $($a$)$

$($b$)$