**Structural Stability and Determinacy Analysis**The following diagrams depict various structural systems. Your task is to analyze each structure to determine its stability and whether it is statically determinate or indeterminate. If a structure is determinate, specify the degree.**Diagram Descriptions:**(a) A simply supported beam with a hinge connection in the middle. There are two supports on either side, and the hinge allows for rotational movement at the center.(b) A frame with multiple support points on each leg and a rectangular configuration. This structure includes a portal frame with three pinned supports at the base.(c) A cantilevered beam connected to a column by a hinge, allowing for rotational movement. The structure has a fixed base at one end and a support with a hinge at the other.(d) A truss-like structure with two hinges on the horizontal beams and diagonal support members. The hinges allow rotational movement at certain points.(e) A horizontal beam fixed at one end with another hinge in the middle, supported by wheels at the other end to allow horizontal movement.**Directions for Analysis:**1. **Determine Stability:** - A stable structure can resist applied loads without undergoing displacement or collapse. - An unstable structure may collapse under load due to lack of sufficient constraints.2. **Determine Static Determinacy:** - A structure is statically determinate if the reaction forces can be calculated using only the equations of static equilibrium (sum of forces and moments equals zero). - A statically indeterminate structure requires additional equations (beyond static equilibrium) for a complete solution.3. **Classify the Degree:** - For determinate structures, note the degree of determinacy, which is how the structure is solved using equilibrium equations alone. Use these criteria to classify each structure and understand their mechanical behavior in practical applications.

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Answered: Classify the shown structures;…

Classify the shown structures; indicating whether stable or unstable. If stable, indicate whether determinate or indeterminate. If determinate, give the degree.

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

Equilibrium and Support Reactions

Civil engineers deal with structures that are composed of several members connected or with individual members such as beams and columns. To analyze such structures, the condition of statics must be applied. Under the static condition, the members are considered to be in equilibrium under the action of forces, that is, the members are assumed to be having negligible velocity.

Question

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**Structural Stability and Determinacy Analysis**

The following diagrams depict various structural systems. Your task is to analyze each structure to determine its stability and whether it is statically determinate or indeterminate. If a structure is determinate, specify the degree.

**Diagram Descriptions:**

(a) A simply supported beam with a hinge connection in the middle. There are two supports on either side, and the hinge allows for rotational movement at the center.

(b) A frame with multiple support points on each leg and a rectangular configuration. This structure includes a portal frame with three pinned supports at the base.

(c) A cantilevered beam connected to a column by a hinge, allowing for rotational movement. The structure has a fixed base at one end and a support with a hinge at the other.

(d) A truss-like structure with two hinges on the horizontal beams and diagonal support members. The hinges allow rotational movement at certain points.

(e) A horizontal beam fixed at one end with another hinge in the middle, supported by wheels at the other end to allow horizontal movement.

**Directions for Analysis:**

1. **Determine Stability:**
- A stable structure can resist applied loads without undergoing displacement or collapse.
- An unstable structure may collapse under load due to lack of sufficient constraints.

2. **Determine Static Determinacy:**
- A structure is statically determinate if the reaction forces can be calculated using only the equations of static equilibrium (sum of forces and moments equals zero).
- A statically indeterminate structure requires additional equations (beyond static equilibrium) for a complete solution.

3. **Classify the Degree:**
- For determinate structures, note the degree of determinacy, which is how the structure is solved using equilibrium equations alone.

Use these criteria to classify each structure and understand their mechanical behavior in practical applications.

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