Hw #4 **Problem Statement:**The 39-lb square plate shown is supported by three vertical wires. Determine the value of \( a \) for which the tension in each wire is equal.**Diagram Explanation:**The diagram shows a square plate with three points labeled \( A \), \( B \), and \( C \). These points represent the attachment of the three supporting wires (not shown in the image) that hold the plate. The square plate has sides of 30 inches. The distances \( a \) marked on the diagram indicate that points \( B \) and \( C \) are symmetrically located along the sides of the plate.**Solution:**- **Construct the FBD (Free Body Diagram):**1. The weight of the plate should be added to the __[blank]__ of the plate, label this point as point G. 2. There are in total __[blank]__ forces and __[blank]__ couples on the FBD.- **Presenting all forces and couples using components:**1. Weight of the plate \( W = (i + [\space] j + [\space] k) \) lb is evenly distributed into three cables, hence:2. Tension on \( A, T_A = (i + [\space] j + [\space] k) \) lb;3. Tension on \( B, T_B = (i + [\space] j + [\space] k) \) lb;4. Tension on \( C, T_C = (i + [\space] j + [\space] k) \) lb.**Note:** The blanks in the solution indicate areas where students need to fill in the appropriate values or concepts as part of the educational exercise. Transcribing the content for an educational website:---### Presenting All Forces and Couples Using Components:1. **Weight of the Plate \( W \) =** \( \square \, i + \square \, j + \square \, k \) (lb) is evenly distributed into three cables, hence:2. **Tension on \( A, \, T_A =** \( \square \, i + \square \, j + \square \, k \) (lb);3. **Tension on \( B, \, T_B =** \( \square \, i + \square \, j + \square \, k \) (lb);4. **Tension on \( C, \, T_C =** \( \square \, i + \square \, j + \square \, k \) (lb);### Taking the Moment About Point A:1. **Position Vectors:** - \( \vec{r}_{AB} = \square \, i + \square \, j + \square \, k \) (in); - \( \vec{r}_{AC} = \square \, i + \square \, j + \square \, k \) (in); - \( \vec{r}_{AG} = \square \, i + \square \, j + \square \, k \) (in);2. **\( \Sigma M_A = 0 \):** - \( M_A^{T_A} = \square \, i + \square \, j + \square \, k \) (lb-in); - \( M_A^{T_B} = \square \, i + \square \, j + \square \, k \) (lb-in); - \( M_A^{T_C} = \square \, i + \square \, j + \square \, k \) (lb-in); - \( M_A^W = \square \, i + \square \, j + \square \, k \) (lb-in);### Equilibrium Equations:1. **\( \Sigma M_A = 0 \):** solve for \( a = \square \) in.--- This transcription provides placeholders (⍰) for values to be filled in, allowing users to complete calculations

Answered: Image /qna-images/answer/d7d232ff-b623-47c3-ba6b-0178ca150a3d.jpg

The 39-lb square plate shown is supported by three vertical wires. Determine the value of a for which the tension in each wire is equal. B 30 in. y Solution: . Construct the FBD A Jeanch 2. There are in total 30 in. 1. The weight of the plate should be added to the → forces and • Presenting all forces and couples using components: 1. Weight of the plate W = 2. Tension on A, TA = 3. Tension on B, TB = 4. Tension on C, Tc = i + i+ i+ i+ j+ + couples on the FB. j+ k (lb); k (lb); ◆ of the plate, lable this point as point G; k (lb); k (lb) is evenly distributed into three cables, hence:

The 39-lb square plate shown is supported by three vertical wires. Determine the value of a for which the tension in each wire is equal. B 30 in. y Solution: . Construct the FBD A Jeanch 2. There are in total 30 in. 1. The weight of the plate should be added to the → forces and • Presenting all forces and couples using components: 1. Weight of the plate W = 2. Tension on A, TA = 3. Tension on B, TB = 4. Tension on C, Tc = i + i+ i+ i+ j+ + couples on the FB. j+ k (lb); k (lb); ◆ of the plate, lable this point as point G; k (lb); k (lb) is evenly distributed into three cables, hence:

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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