Find force in the strut:
Wall is 20 ft high.
Strut begins 4 ft lower, so the "altitude" of strut is 16 ft.
"Base" of strut from wall to end of strut = 8 ft.
strut is 12 ft on center
There is a wind force against wall = 20 lb/ft ^2
Teacher said find wind force:
w = (12 ft)(20 lb/ft^2 ) = 240 lb/ft
Sum MB ???
then find Rt
Rt(16ft) – (w)(20ft)(10ft) =
Rt (16 ft) - (240 lb/ft)(200 ft^2) =
Rt (16 ft) - 48,000 lb/ft =
Rt = 48,000 lb/ft div by 16 ft
Rt = 3000 lb/ft^2
QUESTION:
need to find cos of angle because
cos Ɵ = Rt/Fs
Do I use the base angle of 63.43 degrees or the top angle of 26.57 where the strut connects to the wall?
using cos 63.43 = 0.447290848
Fs (0.447290848) = 3000 lb/ft^2
Fs = 6707.05 lb/ft^2
Using 27.57 degrees for the top angle,
Fs = 3384.30 lb/ft^2
Is either of these correct for finding the force of the strut?
Thank you.
To find the force in the strut, we need to calculate the "strut force" (Fs) using the equation Fs = Rt / cos(θ), where Rt is the force exerted by the wall on the strut and θ is the angle between the wall and the strut.
In your case, you have calculated Rt to be 3000 lb/ft^2. Now, we just need to determine the correct angle (θ) to use in the equation.
The base angle of 63.43 degrees and the top angle of 26.57 degrees you mentioned are the angles between the wall and the strut. However, the correct angle to use in this equation is the angle between the strut and the horizontal ground.
Since the strut is angled downward, we can determine this angle by using the tangent function. The tangent of an angle can be calculated as the ratio of the altitude to the length of the base. In this case, the altitude is 16 ft and the base is 8 ft. So, the tangent of the angle is: tan(θ) = 16 ft / 8 ft = 2.
Next, we will find the angle θ using the inverse tangent function. θ = arctan(2) ≈ 63.43 degrees. Therefore, the correct angle to use in the equation is the base angle of 63.43 degrees. So, we will use cos(63.43) in the equation.
Now, let's calculate the force in the strut (Fs) using the correct angle:
Fs = Rt / cos(63.43) = 3000 lb/ft^2 / cos(63.43) ≈ 3377.18 lb/ft^2.
Based on the calculations, the correct force in the strut is approximately 3377.18 lb/ft^2 when using the base angle of 63.43 degrees.
It's important to note that this calculation assumes an idealized scenario and doesn't take into account other factors like strut stiffness or wind direction. For accurate engineering analysis, additional considerations and calculations may be required.