**Problem 5-80:** The bent rod is supported at points \( A \), \( B \), and \( C \) by journal bearings. Determine the components of reaction at the bearings if the rod is subjected to a 200-pound vertical force and a 30 pound-foot couple moment. The bearings are properly aligned and exert only force reactions on the rod.**Diagram Explanation:**- The diagram shows a three-dimensional view of the bent rod.- The rod has three segments and forms an L-shape with bends at points \( B \) and \( C \).- Journal bearings are present at points \( A \), \( B \), and \( C \).- A 200-pound force is acting downward vertically from point \( B \).- A 30 pound-foot couple moment is applied at the top right segment of the rod at an angle of 45 degrees.- Measurements are provided for the rod's segments: - From \( A \) to \( B \) vertically, a distance of 2 feet. - Between \( B \) and \( C \) horizontally along the x-axis, a distance of 1 foot. - From \( C \) to the end vertically, a distance of 1 foot.**Axes:**- The diagram includes a coordinate system with axes labeled \( x \), \( y \), and \( z \): - Positive \( x \)-axis runs horizontally to the right. - Positive \( z \)-axis runs vertically upwards. - Positive \( y \)-axis runs horizontally backward, into the diagram.

On a rod, a load of 200 lb and a moment of 30 lb-ft are applied. This load and the moment are resisted by journal bearings at A, B, and C. In 3-D journal bearing resists only by 2 perpendicular reactions, reaction along the span of the rod section is taken as zero. To determine the component reactions at the bearings. Ay, AzBx, ByCx, Cz Since it is in 3-D we have 6 equilibrium conditions. Thus, we have 6 variables and 6 equilibrium conditions. The reactions on the bearings are as shown We have 6 equilibrium equations ∑Fx=0Bx+Cx=0 -(1)∑Fy=0 Ay+By=0 -(2)∑Fz=0 Az+Cz-200 =0 -(3) ∑MAx=0-By×1+Cz×1=0 -(4)∑MAy=0-200×2+Bx×1+Cx×3+Cz×2+30cos45° =0 -(5)∑MAz=0 -By×2-Cx×1+30sin45° = 0 -(6) From (5) and (1)-400+2Cx+2Cz+30cos45°=0 -(7)From (4) and (6)-2Cz-Cx+30sin45°=0 -(8)From (7) and (8)Cx=357.57 lbCz=-168.18 lb Thus, Bx=-Cx=-357.57lbBy=Cz=-168.18lbAy=-By=168.18lbAz=-Cz+200 = 168.18+200 =368.18lbThe reaction due to journal bearings Ay=168.18lbAz=368.18lbBx=-357.57lbBy=-168.18lbCx=357.57lbCz=-168.18lb

Engineering

Civil Engineering

*5-80. The bent rod is supported at A, B, and C by journal bearings. Determine the components of reaction at the bearings if the rod is subjected to the 200-lb vertical force and the 30 lb-ft couple moment. The bearings are in proper alignment and exert only force reactions on the rod. 2 ft 1 ft Z 1 ft B ti 200 lb 2 ft 30 lb. ft 45°

*5-80. The bent rod is supported at A, B, and C by journal bearings. Determine the components of reaction at the bearings if the rod is subjected to the 200-lb vertical force and the 30 lb-ft couple moment. The bearings are in proper alignment and exert only force reactions on the rod. 2 ft 1 ft Z 1 ft B ti 200 lb 2 ft 30 lb. ft 45°

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

Braced cuts

The braced cut is a method of providing lateral support to the soil in foundation trenches, to prevent the trenches from deformation by the caving in of soil and resisting it from moving laterally. During shallow excavation in firm soil, generally, slopes are provided to resist the caving in of soil. During shallow excavation in soft soil and deep excavation, the chances of caving in of soil increase. Hence, it becomes necessary to make a provision to resist the deformation of trenches due to caving in of soil. The braced cut is the method used for such conditions. The excavation using braced cuts is a bit uneconomical as compared to the traditional open-cut excavation method but provides better safety than the cut excavation method.

Question

**Problem 5-80:**

The bent rod is supported at points \( A \), \( B \), and \( C \) by journal bearings. Determine the components of reaction at the bearings if the rod is subjected to a 200-pound vertical force and a 30 pound-foot couple moment. The bearings are properly aligned and exert only force reactions on the rod.

**Diagram Explanation:**

- The diagram shows a three-dimensional view of the bent rod.
- The rod has three segments and forms an L-shape with bends at points \( B \) and \( C \).
- Journal bearings are present at points \( A \), \( B \), and \( C \).
- A 200-pound force is acting downward vertically from point \( B \).
- A 30 pound-foot couple moment is applied at the top right segment of the rod at an angle of 45 degrees.
- Measurements are provided for the rod's segments:
- From \( A \) to \( B \) vertically, a distance of 2 feet.
- Between \( B \) and \( C \) horizontally along the x-axis, a distance of 1 foot.
- From \( C \) to the end vertically, a distance of 1 foot.

**Axes:**

- The diagram includes a coordinate system with axes labeled \( x \), \( y \), and \( z \):
- Positive \( x \)-axis runs horizontally to the right.
- Positive \( z \)-axis runs vertically upwards.
- Positive \( y \)-axis runs horizontally backward, into the diagram.

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