$2\mathrm{.}6-16$ Two boards are joined by gluing along a scarf joint, as shown in the figure. For

purposes of cutting and gluing, the angle $$ between the plane of the joint and the faces

of the boards must be between $10$ and $40.$ Under a tensile load $P,$ the normal stress

in the boards is $4\mathrm{.}9$ MPa.

a$.$ What are the normal and shear stresses acting on the glued joint if $=20?$

b$.$ If the allowable shear stress on the joint is $2\mathrm{.}25$ MPa $,$ what is the largest

permissible value of the angle $?$

c$.$ For what angle $$ will the shear stress on the glued joint be numerically equal to

twice the normal stress on the joint?