Handwritten HW #5 ? ? ? https://sisu.instructure.com/courses/1310001/assignments/4888569.submit SJSu Problem 2.101, 2.108, 2.111 Assignments Only problem 2.111 (from the text book) is supposed to be done manually and uploaded on the Canvas. 2.111 A transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. If the tension in wire AB is 840 lb, determine the vertical force P exerted by the tower on the pin at A Grades People Pages Files Syllabus Dashboard 100 ft DA 20 ft Modules Conferences Collaborations Chat Criterion Portfolium SOTE/SOLATE 25 ft 74 ft 20 ft 18 ft File Uploa Google Doc Gogle Drive Upload a file, or choose a file you’ve already uploaded. File: Choose File No file chosen +Add Another File IAb1 P.2png Show allX O Type here to search 3:04 PM PaENG 2/18/2019
transmission tower is held by three guy wires attached to a pin at A and anchored by bolts at B, C, and D. If the tension in wire AC is 840 lb, determine the vertical force P exerted by the tower on the pin at A…..
The correct answer and explanation is:
Final Answer:
The vertical force P is approximately 220 lb.
Explanation:
In this problem the transmission tower is stabilized by three guy wires, one of which (wire AC) has a tension of 840 lb. To find the vertical force P that the tower exerts on the pin at A, we first focus on the vertical component of the tension in wire AC. Because the guy wires are inclined, their tensions must be resolved into vertical and horizontal components. In our case, only the vertical component from wire AC contributes to supporting the tower’s load vertically.
The geometry provided tells us that the point where wire AC is anchored (point C) lies horizontally 74 ft from A, and the tower’s height (or vertical rise from A to the level of the anchor) is 20 ft. Using the Pythagorean theorem, we find the length L of the wire:
L = √(20² + 74²) ≈ √(400 + 5476) ≈ √5876 ≈ 76.66 ft.
The angle θ between the wire and the horizontal satisfies
tan θ = 20/74,
so the sine of the angle (which gives the ratio of the vertical component to the tension) is
sin θ = 20/76.66 ≈ 0.261.
Multiplying the tension by sin θ gives the vertical component:
T_v = 840 lb × 0.261 ≈ 219 lb.
Since the vertical equilibrium at the pin A requires that the upward component of the guy wire’s tension be balanced by the downward reaction P of the tower (or vice versa, depending on sign convention), the vertical force exerted by the tower on the pin must be approximately 219 lb. Rounding for practical purposes, we state P ≈ 220 lb.
This analysis is fundamental in structural mechanics: resolving forces into components allows engineers to ensure that the structure remains in static equilibrium under the applied loads. Accurate calculation of these forces is crucial for safety and stability in the design of structures such as transmission towers.
Diagram:
A (Tower Top)
●
|\
| \ T = 840 lb (wire AC)
20ft| \
| \
| \
●-----● C (Anchor)
(A to C = 74 ft horizontally)