S21A- STATIKA PORTAL 3 SENDI- REAKSI PERLETAKAN

Summary

This video explains the process of solving a structural analysis problem for a statically indeterminate three-jointed portal. The presenter demonstrates how to calculate reaction forces and internal forces using equilibrium equations, focusing on horizontal and vertical forces, as well as moments. The method involves dividing the structure, applying equilibrium conditions, and calculating unknown forces at various points. Through a series of calculations, the video shows how to solve for the forces, moments, and verify results, providing a step-by-step guide for analyzing statically indeterminate structures in civil engineering.

Takeaways

• 😀 The topic is about solving structural problems related to a 'three-joint portal structure,' also known as a 'portal three-joint frame.'
• 😀 The structure in question is classified as statically indeterminate because there are four unknown forces, which makes it impossible to solve using standard static equilibrium methods.
• 😀 To make the problem solvable, a joint (or 'sendi') is added to the center of the portal structure, allowing it to rotate and behave as a statically determinate structure.
• 😀 The added joint allows for the application of the principles of static determinacy, making the structure behave more like a system that can rotate and not be rigid like an indeterminate structure.
• 😀 The speaker begins by calculating the reactions at the supports of the portal structure, using equilibrium equations for both horizontal (Sigma FX = 0) and vertical (Sigma FY = 0) forces.
• 😀 The script emphasizes that when calculating the reactions, positive directions are assumed for forces moving upward or to the right, and counterclockwise moments are considered positive.
• 😀 For distributed loads (Q1 and Q2), these are first converted into point loads to simplify the calculations, which are then used in the equilibrium equations.
• 😀 The speaker uses the principle of static equilibrium for moments (Sigma MA and Sigma MB) to calculate unknown reaction forces at specific points in the structure.
• 😀 The use of the Sigma MA and Sigma MB helps to solve for unknowns in complex static systems where there are multiple forces acting on the structure.
• 😀 The final results are verified by checking the calculated forces (e.g., AX and BX) against the equilibrium equation for horizontal forces (Sigma FX = 0) to ensure the calculations are correct.
• 😀 The process involves a careful and systematic breakdown of the structural elements, ensuring that all forces and moments are accounted for, and checks are made to confirm the accuracy of the results.

Q & A

What is a portal frame with three joints?

A portal frame with three joints is a type of structural system used in civil engineering, where a frame has three connection points, usually consisting of two vertical members and a horizontal beam. This type of structure is statically indeterminate when it has more unknown forces than the number of available equilibrium equations.

Why is the structure considered statically indeterminate?

The structure is considered statically indeterminate because it has four unknown forces, which exceed the number of available equilibrium equations (which is typically three). This makes it impossible to solve using basic static equilibrium alone.

How does adding a hinge in the middle of the structure help solve the problem?

Adding a hinge in the middle of the structure changes its properties by allowing rotational movement at that joint. This introduces additional unknowns that simplify the analysis and allows the structure to be treated as statically determinate, making it solvable with conventional methods.

What are the unknown forces in the portal frame problem?

The unknown forces in this portal frame problem are the reaction forces at the supports: AX (horizontal reaction at point A), AY (vertical reaction at point A), BX (horizontal reaction at point B), and BY (vertical reaction at point B).

What does the equilibrium equation ΣFX = 0 represent?

The equilibrium equation ΣFX = 0 represents the balance of forces in the horizontal direction. It ensures that the sum of all horizontal forces acting on the structure is zero, meaning there is no net horizontal force causing motion.

How is the distributed load Q1 converted into a point load?

The distributed load Q1, which is uniformly distributed along a segment of the beam, is converted into a point load by multiplying the load intensity (100 kg/m) by the length of the segment (7 meters). This results in a point load of 700 kg.

What does the equilibrium equation ΣFY = 0 represent?

The equilibrium equation ΣFY = 0 represents the balance of forces in the vertical direction. It ensures that the sum of all vertical forces acting on the structure is zero, meaning there is no net vertical force causing motion.

How are moments used to calculate the reactions in the structure?

Moments are used by calculating the rotational effects of forces about a particular point (such as the base of the structure). The sum of moments around a point must be zero (ΣM = 0) for the structure to be in equilibrium. This allows the calculation of unknown forces like AY and BY by considering their effect on the rotation of the structure.

What is the significance of checking the results by plugging them into the equilibrium equations?

Checking the results by plugging them back into the equilibrium equations ensures that the calculated forces satisfy all the conditions of equilibrium. This verification process confirms the correctness of the solution and ensures that the forces and moments are balanced.

How are the final reaction forces AX, BX, AY, and BY determined?

The final reaction forces AX, BX, AY, and BY are determined by solving the system of equilibrium equations. These equations are based on the forces and moments acting on the structure, and solving them gives the values of the unknown forces, which are checked for consistency to ensure accuracy.