Mekanika Bahan - Tegangan Lentur

Summary

This video lecture on Material Mechanics focuses on the concept of bending stress in beams. It begins by explaining the definition of deflection and bending stress, with a formula for calculating bending stress. The video walks through a step-by-step example of calculating bending stress in a beam subjected to a concentrated load. Key concepts such as moment of inertia, modulus of elasticity, and maximum bending stress are discussed in detail. The instructor also illustrates the calculation of both maximum compressive and tensile stresses. The lecture concludes with practice problems to reinforce understanding, encouraging active learning through problem-solving.

Takeaways

• 😀 The lecture is about material mechanics, focusing on bending stress and deflection of beams under centralized loads.
• 😀 The deflection (devi) of a beam is defined as the displacement of a point from its original position, measured in the direction of the load.
• 😀 Bending stress is calculated using the formula: Sigma = M * y / I, where M is the moment, y is the distance from the neutral axis, and I is the moment of inertia of the beam's cross-section.
• 😀 To calculate bending stress, it’s essential to first determine the moment of inertia for the beam's cross-section.
• 😀 For this example, the beam's cross-section consists of two large square sections and smaller ones, each with specific dimensions for which the moment of inertia is calculated.
• 😀 The centroid (center of mass) of the beam's cross-section is crucial for calculating bending stress, and for symmetrical sections, this is typically at the center of the cross-section.
• 😀 The maximum moment for the beam is calculated based on the applied load and the beam's span, using the formula M = P * L / 4.
• 😀 Maximum bending stress occurs at the farthest point from the neutral axis, which is typically at the top or bottom of the beam depending on the direction of the applied load.
• 😀 In the example, the maximum bending stress (compressive or tensile) is calculated at a specific point on the beam using the formula Sigma = M * y / I.
• 😀 The lecture also discusses how to calculate bending stress at a specific point (y1), given the distance from the neutral axis and using the previously calculated moment and moment of inertia.
• 😀 The task encourages solving additional problems involving beams with uniform loads and concentrated loads, reinforcing the understanding of bending stress and deflection calculations.

Q & A

What is the definition of deflection in beam mechanics?

Deflection refers to the displacement of a point from its original position when a force is applied to a beam, causing it to bend. It is measured in the direction of the applied force.

What is the formula for calculating bending stress (σ) in a beam?

The formula for bending stress is σ = M * y / I, where M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia of the beam's cross-sectional area.

How do you calculate the moment of inertia (I) of a cross-section made up of two different types of rectangles?

The moment of inertia of a composite cross-section is calculated by finding the individual moments of inertia of each rectangle, then subtracting the moment of inertia of the smaller rectangle from that of the larger one, considering their distances from the neutral axis.

Why is the center of gravity (CG) of the two rectangles taken as zero in the calculation of bending stress?

The center of gravity (CG) of the two rectangles is taken as zero because the composite cross-section is symmetric, and the CGs of the individual rectangles align at the neutral axis, making their contribution to the moment of inertia effectively null.

What is the significance of the maximum bending moment (M) in calculating bending stress?

The maximum bending moment (M) is crucial because it represents the highest internal moment in the beam, occurring at the point of maximum bending. It directly affects the magnitude of the bending stress, which is highest where M is largest.

How do you calculate the maximum bending stress at a point on the beam?

To calculate the maximum bending stress, use the formula σ = M * y / I, where M is the maximum moment, y is the maximum distance from the neutral axis (which is the outermost fiber), and I is the moment of inertia of the cross-section.

What is the relationship between bending stress and the position on the beam (e.g., at maximum and minimum bending moments)?

Bending stress varies depending on the location on the beam. At points where the bending moment is maximum, the stress is also at its highest. Conversely, at points with zero bending moment, such as the center of a simply supported beam under load, the bending stress is zero.

What happens to the bending stress if the beam's cross-section is symmetric?

If the beam's cross-section is symmetric, the bending stress will be identical in magnitude but opposite in direction on either side of the neutral axis, meaning the maximum compressive and tensile stresses will have the same value but will occur on opposite sides of the neutral axis.

How is the bending stress calculated for a point located away from the center of the beam?

To calculate the bending stress at a point away from the center, the bending moment at that point is used in the formula σ = M * y / I, where y is the distance from the neutral axis to the point being analyzed.

What does the term 'neutral axis' refer to in beam mechanics?

The neutral axis in beam mechanics is the axis along the beam that experiences no longitudinal strain during bending. It lies at the midpoint of the beam's cross-section in the direction of the applied force.