09-06 Tegangan geser pada balok: contoh perhitungan

Summary

This transcript provides a detailed explanation on how to calculate shear stress in a structural beam subjected to a shear force of 5 kN. The discussion includes determining the moment of inertia, calculating the first moment of area, and understanding the geometry of the section at different points (A, B, C, D). Various calculations are performed step-by-step, including determining the shear stress at each point, and the impact of the beam's structural characteristics such as the location of centroids and the first moment of area. The overall focus is on calculating the shear stress across different sections of the beam.

Takeaways

• 😀 The problem involves calculating shear stress for a rectangular cross-section subjected to a shear force of 5 kN.
• 😀 The cross-section dimensions are 300 mm by 400 mm, and the shear force is applied to this section.
• 😀 The shear force is divided into points A, B, C, and D for calculation purposes, with specific distances and moments provided for each point.
• 😀 The moment of inertia (I) for the section is calculated using the formula based on the section’s dimensions.
• 😀 The first moment of area (Q) is important for calculating the shear stress and is derived from the geometry of the cross-section.
• 😀 For the upper section of the beam (above point A), the shear stress is calculated to be zero, as the first moment of area above this point is zero.
• 😀 The shear stress at point B is non-zero and calculated based on the distribution of shear force and the moment of inertia.
• 😀 The distance to the centroid of the section and the moment arms are crucial in calculating the first moment of area for shear stress.
• 😀 For the section under consideration, the values of Q and I are used to compute the shear stress at various points (B, C, D).
• 😀 The shear stress is calculated using the formula τ = VQ / (Ib), where V is the shear force, Q is the first moment of area, I is the moment of inertia, and b is the width at the point of interest.
• 😀 The script demonstrates that the shear stress varies along the section, being zero at the top and increasing as you move down, with a peak at point B and similar values at points C and D.

Q & A

What is the dimension of the cross-section discussed in the script?

The cross-section has dimensions of 300 mm by 400 mm.

What is the shear force applied to the cross-section?

A shear force of 5 kN is applied to the cross-section.

What is the general method used to calculate shear stress in this context?

The shear stress is calculated using the formula τ = (V * Q) / (I * b), where V is the shear force, Q is the first moment of area, I is the moment of inertia, and b is the width of the section.

What is the significance of the first moment of area (Q) in shear stress calculation?

The first moment of area (Q) is used to determine the distribution of shear stress across different points of the cross-section, reflecting how far the area is from the centroid.

Why is the shear stress at point A zero?

The shear stress at point A is zero because the first moment of area above this point is zero, meaning there is no area to contribute to the shear force above it.

What is the role of the moment of inertia (I) in calculating shear stress?

The moment of inertia (I) represents the distribution of area in the cross-section relative to the neutral axis, and it influences the resistance of the section to bending and shear. It is used to calculate the shear stress at different points.

How is the shear stress at points B and C different from point A?

The shear stress at points B and C is non-zero because the first moment of area (Q) is non-zero at these points, while at point A, the area above it does not contribute to shear force.

Why is the shear stress calculated at specific points along the cross-section (e.g., points B, C, D)?

The shear stress varies across the height of the section, so it is calculated at specific points (B, C, D) to understand how shear stress distributes across the cross-section.

What is the calculation for the first moment of area at point B?

At point B, the first moment of area is calculated by multiplying the area of the section above point B by the distance from the centroid of that area to the neutral axis.

What happens to the shear stress as you move down the section (from A to D)?

As you move down the section from A to D, the shear stress varies, with the stress being zero at point A, increasing at points B and C, and remaining constant at point D due to the absence of further shear force contributions.