Find the tensile capacity P1 for the single-shear lap connection shown below Bolts are 3/4-in-diameter high-strength bolts..All structural steel is A36. Assume that the connection is A325SC.Assume a class A contact surface and a slip-critical connection. 12" xt" plate iedge distance (typ.) The properties of the steel are as follows: The tensile strength, Fu,ofA36 steel is 58 ksi, and the allowable shear stress F=17.0 ksi The cross-sectional area of the bolt Ab=0.44I in².

To find the tensile capacity P1 for the single-shear lap connection, we need to calculate the strength of the bolts and the strength of the plate.

Strength of Bolts:

The ultimate strength of the bolts is determined by the minimum of the following:

1. Bolt shear strength
2. Bolt bearing strength
3. Bolt tensile strength

Bolt Shear Strength:

The bolt shear strength is given by:

Vn = 0.6*Fy*Ab

where Vn is the nominal shear strength of the bolt, Fy is the yield strength of the bolt material, and Ab is the cross-sectional area of the bolt.

Substituting the given values, we get:

Vn = 0.6*90*0.44 = 23.76 kips

Bolt Bearing Strength:

The bolt bearing strength is given by:

Rn = 2.4*dt*t*Fyb

where Rn is the nominal bearing strength of the bolt, dt is the thickness of the connected material, t is the thickness of the bolt head or nut, and Fyb is the yield strength of the bolt material.

Substituting the given values, we get:

Rn = 2.4*0.75*0.75*90 = 121.5 kips

Bolt Tensile Strength:

The bolt tensile strength is given by:

Tn = 0.75*Fub*Ab

where Tn is the nominal tensile strength of the bolt, Fub is the ultimate strength of the bolt material, and Ab is the cross-sectional area of the bolt.

Substituting the given values, we get:

Tn = 0.75*120*0.44 = 29.7 kips

The minimum of the above three values is the ultimate strength of the bolt, which is 23.76 kips.

Strength of Plate:

The ultimate strength of the plate is determined by the minimum of the following:

1. Plate tensile strength
2. Plate bearing strength
3. Plate yielding strength

Plate Tensile Strength:

The plate tensile strength is given by:

Pu = Fu*Ap

where Pu is the ultimate strength of the plate, Fu is the ultimate strength of the plate material, and Ap is the effective net area of the plate.

The effective net area of the plate is given by:

Ap = An - n*d*(dh + 0.5*t)

where An is the gross area of the plate, n is the number of bolts, d is the bolt diameter, dh is the diameter of the hole, and t is the thickness of the connected material.

Substituting the given values, we get:

An = 12*1 = 12 in²
n = 4
d = 0.75 in
dh = 0.8125 in (assuming 1/16 in oversize hole)
t = 1 in

Ap = 12 - 4*0.75*(0.8125 + 0.5*1) = 5.25 in²

Substituting the given values, we get:

Pu = 58*5.25 = 304.5 kips

Plate Bearing Strength:

The plate bearing strength is given by:

Rn = 2.4*dt*t*Fyb

where Rn is the nominal bearing strength of the plate, dt is the thickness of the connected material, t is the thickness of the bolt head or nut, and Fyb is the yield strength of the bolt material.

Substituting the given values, we get:

Rn = 2.4*1*0.75*36 = 64.8 kips

Plate Yielding Strength:

The plate yielding strength is given by:

Py = 0.9*Fy*Ag

where Py is the yielding strength of the plate, Fy is the yield strength of the plate material, and Ag is the gross area of the plate.

Substituting the given values, we get:

Ag = 12*1 = 12 in²

Py = 0.9*36*12 = 388.8 kips

The minimum of the above three values is the ultimate strength of the plate, which is 64.8 kips.

Now, we can find the tensile capacity P1 of the connection by taking the minimum of the ultimate strength of the bolts and the ultimate strength of the plate.

P1 = min(23.76, 64.8) = 23.76 kips

Therefore, the tensile capacity P1 for the single-shear lap connection is 23.76 kips.