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Consider the structure below. Using virtual work, compute the vertical displacement at point C. 30 kN B 5 m 4 m E=200 GPa I=300(106) mmª 60 kNm

Consider the structure below. Using virtual work, compute the vertical displacement at point C. 30 kN B 5 m 4 m E=200 GPa I=300(106) mmª 60 kNm

Structural Analysis
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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**Question 7** Consider the structure below. Using virtual work, compute the vertical displacement at point C. The diagram is a structure with the following details: 1. A vertical beam, AB, with a length of 5 meters. 2. A horizontal beam, BC, with a length of 4 meters. 3. Point A is fixed to the ground. 4. A horizontal force of 30 kN is applied at point B. 5. A moment of 60 kNm is applied at point C, acting clockwise. 6. The material properties are given as: - Modulus of Elasticity, \(E = 200 \text{ GPa}\). - Moment of Inertia, \(I = 300 \times 10^6 \text{ mm}^4\). The task is to find the vertical displacement at point C using the method of virtual work.
Transcribed Image Text:**Question 7** Consider the structure below. Using virtual work, compute the vertical displacement at point C. The diagram is a structure with the following details: 1. A vertical beam, AB, with a length of 5 meters. 2. A horizontal beam, BC, with a length of 4 meters. 3. Point A is fixed to the ground. 4. A horizontal force of 30 kN is applied at point B. 5. A moment of 60 kNm is applied at point C, acting clockwise. 6. The material properties are given as: - Modulus of Elasticity, \(E = 200 \text{ GPa}\). - Moment of Inertia, \(I = 300 \times 10^6 \text{ mm}^4\). The task is to find the vertical displacement at point C using the method of virtual work.
The table shown is for the integration of the product of two shapes with a common length \( L \), denoted as \(\int_0^L M Q \, dx\). The values in the table represent this integration. The rows and columns signify different geometric shapes, and the table entries provide the formulas for integration where these shapes interact. The shapes include rectangles, triangles, trapezoids, and parabolas with different orientations. ### Columns: - **Rectangle:** - Illustrated by a rectangle with base \( L \) and height \( Q \). - **Triangle:** - Three configurations are given, characterized by their bases \( L \) and the respective vertex positions. - **Trapezoid:** - Depicted with bases \( L \) and side \( Q_2 \). ### Rows: - **Rectangle:** - Simple rectangle displayed vertically with height \( M \) and base \( L \). - **Triangle:** - Several configurations presented, varying in orientation and height \( M \). - **Trapezoid:** - Shown with two parallel sides \( M \) and \( M_1 \). - **Parabola:** - Multiple configurations both concave up and down, each depicting a slope attribute. ### Table Entries: The table entries specify integral solutions for the interactions: - For example, Rectangle-Rectangle: \(\frac{LMQ}{2}\) - Triangle-Triangle: \(\frac{LMQ}{6}\) and \(\frac{LMQ}{3}\) - Trapezoid interactions contain different configurations leading to formulas like \(\frac{LQ}{6}(2M_1 + M)\). ### Explanation of Symbols: - \( M, M_1 \): Heights of the shapes. - \( Q, Q_2 \): Base lengths of the shapes. - Formulas appear with combinations of these variables and constants, indicating how areas multiply and integrate over the length \( L \). This table serves as a reference for solving problems involving integrals of geometric shape products, primarily applied in fields such as engineering and physics.
Transcribed Image Text:The table shown is for the integration of the product of two shapes with a common length \( L \), denoted as \(\int_0^L M Q \, dx\). The values in the table represent this integration. The rows and columns signify different geometric shapes, and the table entries provide the formulas for integration where these shapes interact. The shapes include rectangles, triangles, trapezoids, and parabolas with different orientations. ### Columns: - **Rectangle:** - Illustrated by a rectangle with base \( L \) and height \( Q \). - **Triangle:** - Three configurations are given, characterized by their bases \( L \) and the respective vertex positions. - **Trapezoid:** - Depicted with bases \( L \) and side \( Q_2 \). ### Rows: - **Rectangle:** - Simple rectangle displayed vertically with height \( M \) and base \( L \). - **Triangle:** - Several configurations presented, varying in orientation and height \( M \). - **Trapezoid:** - Shown with two parallel sides \( M \) and \( M_1 \). - **Parabola:** - Multiple configurations both concave up and down, each depicting a slope attribute. ### Table Entries: The table entries specify integral solutions for the interactions: - For example, Rectangle-Rectangle: \(\frac{LMQ}{2}\) - Triangle-Triangle: \(\frac{LMQ}{6}\) and \(\frac{LMQ}{3}\) - Trapezoid interactions contain different configurations leading to formulas like \(\frac{LQ}{6}(2M_1 + M)\). ### Explanation of Symbols: - \( M, M_1 \): Heights of the shapes. - \( Q, Q_2 \): Base lengths of the shapes. - Formulas appear with combinations of these variables and constants, indicating how areas multiply and integrate over the length \( L \). This table serves as a reference for solving problems involving integrals of geometric shape products, primarily applied in fields such as engineering and physics.
Expert Solution
Step 1

Given:

A frame with loading on it 

E = 200 GPa, I = 300*10⁶mm⁴

Required:

Vertical displacement at C

 

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