Three$-$bar truss ABC $($see figure$)$ is constructed of steel pipes having a cross$-$sectional area $A=4,300m{m}^2$ and a modulus of elasticity $E=210$GPa.

Member $BC$ is of length $L=2\mathrm{.}1m,$ and the angle between members $AC$ and $AB$ is known to be $60.$ Member $AC$ length is $b=0\mathrm{.}71L.$ Loads $P=140kN$ and $2P=280kN$ act vertically and horizontally at joint $C,$ as shown. Joints A and $B$ are pinned supports. $($Use the law of sines and law of cosines to find missing dimensions and angles in the figure. Due to the nature of this problem, do not use rounded intermediate values$-$including answers submitted in WebAssign$-$in your calculations.$)$

$($a$)$ Find the support reactions at joints A and $B($in kN $).$ Use horizontal reaction $B_x$ as the redundant. $($Include the signs of the values in your answers.$)$

$A_x=$

Your response differs from the correct answer by more than $100\%kN$

$A_y=$

Your response differs from the correct answer by more than $10\%.$ Double check your calculations. kN

$B_x=$

$B_y=$

The correct answer is not zero. kN

Your response differs from the correct answer by more than $10\%.$ Double check your calculations. kN

$($b$)$ What is the maximum permissible value of load variable $P$ if the allowable normal stress in each truss member is $150$ MPa $?($Enter the magnitude in kN $.)$

kN