Statics cantilever beam at angle with load

[dreeve]

Homework Statement

Design a bolted joint to attach a suitable American Standard Steel channel at a 15 degree angle to store the bundle of nominal 8 inch diameter x 30 feet long seamless wrought steel pipe. An identical member 20 feet away supports the other end of the bundle. The bundles may vary from center by 1.5 feet. The W18X55 vertical members and the channels are made from ASTM A36 steel.

Homework Equations

I know how to determine the bolts once I figure out the force. I am having trouble determining the effect the 15 degree angle has. The pipes way a total of ~6000lb. To figure out the resulting force on the cantilever beam F_y do I just use

F_y = 6000lb (cos) 15 = 5795.55 lb
F_x = 6000lb (sin) 15 = 1552.91 lb

AGAIN I don't need any help on determing what bolts to use, I just need help finguring out the resultant force acting on the cantilever beam with the angle, I can't find any example problems like this.

I really appreciate any help guys, this is a take home quiz due in about a week, My teacher did a horrible job of teaching statics.

The Attempt at a Solution

 

[KataKoniK]

Hello,

Thank you for your question. Designing a bolted joint for a specific application can be a complex task, but I will try to provide some guidance on how to approach this problem.

First, let's break down the problem into smaller parts. We have a cantilever beam (the W18X55 vertical member) and a channel that needs to be attached at a 15 degree angle to support the bundle of pipes. The other end of the bundle is supported by an identical member 20 feet away.

To determine the forces acting on the cantilever beam, we need to consider the weight of the bundle of pipes and the reaction forces from the other end of the bundle.

The weight of the bundle can be calculated as follows:

Weight = (weight per foot) x (length of pipes)

Weight per foot = (pi/4) x (diameter)^2 x (density of steel)

Plugging in the given values, we get:

Weight per foot = (3.14/4) x (8 inches)^2 x (490 lbs/ft^3) = 153.94 lbs/ft

Weight of bundle = (153.94 lbs/ft) x (30 ft) = 4618.2 lbs

Next, we need to consider the reaction forces from the other end of the bundle. Since the other end is supported by an identical member, we can assume that the reaction forces will be equal and opposite to the weight of the bundle.

Now, let's consider the effect of the 15 degree angle. The angle will cause a component of the force to act in the horizontal direction (Fx) and a component to act in the vertical direction (Fy).

To determine these forces, we can use trigonometric relationships.

Fx = Weight of bundle x cos(15 degrees) = 4618.2 lbs x cos(15 degrees) = 4446.6 lbs

Fy = Weight of bundle x sin(15 degrees) = 4618.2 lbs x sin(15 degrees) = 1202.9 lbs

These forces will act at the point where the channel attaches to the cantilever beam.

To design the bolted joint, we need to consider the shear and tension forces acting on the bolts. The shear force will be equal to the horizontal component (Fx) and the tension force will be equal to the vertical