EXAMPLE 1.3.5. COMBINED STRESSES IN A SYSTEM

A steel strut S serving as a brace for a boat hoist transmits a compressive foce P=12kips to the deck of a pier as shown. The strut has a hollow square cross section with wall thickness t= 0.375in. and the angle  between the strut and the horizontal is . A pin through the strut transmits the compressive force from the strut to two gussets G that are welded to the base plate B. Four anchor bolts fasten the base plate to the deck.

The diameter of the pin is , the thickness of the gussets is , the thickness of the base plate is , and the diameter of the anchor bolts is

Determine the following stresses:

1. The bearing stress  between the strut and the pin,
2. The shear stress in the pin
3. The bearing stress between the pin and the gussets
4. The bearing stress between the anchor bolts and the base plate
5. The shear stress in the anchor bolts

(Disregard any friction between the base plate and the deck.)

There is only one formula used to solve the stress. The only things considered are the application of the force to the area considered.

                

                   

1. The bearing stress between the strut and the pin.

Check on the plan (b), regardless of the inclination of the strut (any angle applied), the pin will still be acting perpendicular to the strut. Hence, the two parameters are:

load:  

For the area, bearing stress requires the contact area between the strut and the pin. The contact area is the projected area between the two materials.

The contact area is taken as the thickness of the strut and the diameter of the pin.

Hence, 


By using these two parameters:

2. The shear stress in the pin

The pin will have to crack on two points where the strut is applying force.

The shear plane is the cross-sectional area of the pin.





So, with these parameters, the shear stress of the pin can be solved as:

3. The bearing stress between the pin and the gusset

For the bearing stress between the pin and the gussets, the inclination of the load does not matter because of the circular surface of the pin.

The area will be computed as follows:




The bearing stress between the pin and the gussets are solved as:

4. The bearing stress between the anchor bolts and the base plate

In order to solve the bearing stress between the anchor bolts and the base plate, the force applied should cause the contact between the two materials. That contact will occur when the force is applied to the base plate in a manner similar to sliding from the foundation (hence the use of anchor bolts).

For load:




For the area, there are 4 anchor bolts holding the base plate.











Thus, the bearing stress can be solved:

5. The shear stress in the anchor bolts

For the anchor bolt to shear, the cross-section is considered with the applied load parallel to the axis of the base plate.






So, the shear stress becomes: