In the steel structure shown, a 6-mm-diameter pin is used at C and 10-mm-diameter pins are used at B and D. The ultimate shearing stress is 150 MPa at all connections, and the ultimate normal stress is 400 MPa in link BD. Knowing that a factor of safety of 3.0 is desired, determine the largest load P that can be applied at A. Note that link BD is not reinforced around the pin holes.
Fig. P1.66
The largest load P that can be applied at A.
Answer to Problem 66RP
The largest load P that can be applied at A is
Explanation of Solution
Given information:
The diameter of the pin at C is
The diameter of the pin at B and D is
The ultimate normal stress
The ultimate normal stress
The factor of safety is 3.0.
Calculation:
Sketch the free body diagram of ABC as shown in Figure 1.
Refer to Figure 1.
Taking moment about C.
Taking moment about B
Find the area of tension on net section of link BD using the relation:
Here, t is the thickness of the section,
Substitute
Find the force in member BD on net section of link BD using the relation:
Here,
Modify Equation (4).
Substitute
Find the area of shear in pins BD using the relation:
Substitute
Find the force in member BD shear in pins BD using the relation:
Here,
Modify Equation (7).
Substitute
Select the smaller value of
Find the value of P as follows:
Substitute
Find the shear in pin at C using the relation:
Substitute
Find the value of C shear in pins C using the relation:
Here,
Modify Equation (10).
Substitute
Find the largest load P such that be applied at A.
Substitute
Select the smaller value of P.
Thus, the largest load P such that be applied at A is
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