Determine the magnitude of the pin force at C given θ = 23° and P = 52 lbs. This image presents a mechanical linkage diagram consisting of multiple connected bars labeled A, B, C, D, E, and F. The setup illustrates a complex linkage system attached to a vertical wall on the left side of the diagram.**Description of Components and Geometry:**- **Bar A** is fixed horizontally to the vertical wall, measuring 8 inches in height from the base where it connects.- **Bar B** connects perpendicularly to the top of Bar A, extending horizontally for 2 inches.- **Bar C** is connected to Bar B and extends vertically downwards, parallel to Bar A.- **Bar D** is connected to the right end of Bar B, extending horizontally for 12 inches. A joint or pivot point, labeled as J, is located 6 inches along Bar D from the left side.- **Bar E** is connected to the right end of Bar D, forming a toggle mechanism with Bar C.- **Bar F** is the final section, extending from the rightmost pivot point with a rotational motion indicated by a red arrow. The angular movement of Bar F is denoted by the Greek letter theta (θ).**Measurements:**- The horizontal sections, namely B and D, measure 4 inches and 12 inches, respectively.- The joint J in Bar D is precisely midway at 6 inches from the starting point at the left.- Despite the intricate design, all bars appear to be interconnected with pivot joints allowing rotational movement at each connection point.- An angled force or motion is applied at point F, indicated by the letter P, demonstrating the mechanical interaction controlled by angle θ.This diagram serves as a detailed study of mechanical linkage, showcasing the movement and force transmission properties of such systems in applied mechanics.

P = 52 lbs θ = 23o ∑Fx = 0HE = PsinθHE = 52sin23HE = 20.32 lbs∑Fy = 0RE = PcosθRE = 52cos23RE = 47.87 lbs∑Fx = 0HC = HEHC = 20.32 lbs∑Fy = 0RC = RERC = 47.87 lbs

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Engineering

Civil Engineering

Determine the magnitude of the pin force at C given θ = 23° and P = 52 lbs.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

Determine the magnitude of the pin force at C given θ = 23° and P = 52 lbs.

This image presents a mechanical linkage diagram consisting of multiple connected bars labeled A, B, C, D, E, and F. The setup illustrates a complex linkage system attached to a vertical wall on the left side of the diagram.

**Description of Components and Geometry:**

- **Bar A** is fixed horizontally to the vertical wall, measuring 8 inches in height from the base where it connects.
- **Bar B** connects perpendicularly to the top of Bar A, extending horizontally for 2 inches.
- **Bar C** is connected to Bar B and extends vertically downwards, parallel to Bar A.
- **Bar D** is connected to the right end of Bar B, extending horizontally for 12 inches. A joint or pivot point, labeled as J, is located 6 inches along Bar D from the left side.
- **Bar E** is connected to the right end of Bar D, forming a toggle mechanism with Bar C.
- **Bar F** is the final section, extending from the rightmost pivot point with a rotational motion indicated by a red arrow. The angular movement of Bar F is denoted by the Greek letter theta (θ).

**Measurements:**

- The horizontal sections, namely B and D, measure 4 inches and 12 inches, respectively.
- The joint J in Bar D is precisely midway at 6 inches from the starting point at the left.
- Despite the intricate design, all bars appear to be interconnected with pivot joints allowing rotational movement at each connection point.
- An angled force or motion is applied at point F, indicated by the letter P, demonstrating the mechanical interaction controlled by angle θ.

This diagram serves as a detailed study of mechanical linkage, showcasing the movement and force transmission properties of such systems in applied mechanics.

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