Beton Prategang :"Desain Lentur Balok Prategang - Soal & Pembahasan"-Fast Learning#umb#prestressing

Summary

This lecture focuses on the design and analysis of prestressed concrete beams under bending. It begins with fundamental concepts, emphasizing that stresses in the beam must remain below allowable material limits during both transfer and service stages. The session then walks through a detailed example, calculating concrete stresses, moments from dead and live loads, and the required prestressing force. It also determines the number of tendons needed, considering tendon specifications and eccentricity. The lecturer checks the results against design standards, confirming safety and efficiency. The session concludes by highlighting potential adjustments for different concrete strengths or additional loads, providing a practical, step-by-step guide to prestressed beam design.

Takeaways

• 😀 The video covers **flexural prestressed beam design** with both concept explanation and problem-solving examples.
• 😀 Prestressed beams experience **uniform and concentrated loads**, including self-weight, which must be accounted for in design.
• 😀 Concrete stress must remain **below allowable limits** based on SNI standards for both **transfer and service phases**.
• 😀 The **allowable concrete stresses** according to SNI are: transfer (compression 0.6f_ck, tension 0.25f_ck) and service (compression 0.45f_ck, tension 0.5√f_ck).
• 😀 The calculation process involves determining **stress at transfer and service stages**, considering dead load, live load, and prestressing effects.
• 😀 **Beam dimensions** and material properties (concrete f_ck, tendon f_pu) are essential inputs for calculating stresses and tendon requirements.
• 😀 **Section properties**, including area and moment of inertia (S_x), are used to evaluate total stresses in the beam using the formula σ = -P/A ± Pe/Sx ± M/Sx.
• 😀 The **prestressing force** must be adjusted for losses, here assumed as 20%, to ensure accurate design and tendon count.
• 😀 In the example, **five tendons** are required per beam section using ST416 tendons with specified ultimate tensile strength.
• 😀 The approach can be adapted for **different concrete strengths** (e.g., f_ck = 35 MPa) and prestressing forces while maintaining safety and serviceability.
• 😀 The service stage calculations include **both dead load and live load**, whereas transfer stage only considers dead load.
• 😀 Checking **tensile and compressive stresses at top and bottom fibers** ensures the design remains within permissible limits throughout the beam's life.

Q & A

What is the primary concept of prestressed concrete beam design discussed in the transcript?

The primary concept is that the prestressed concrete beam must have the stresses induced by applied loads be less than the allowable stresses of the concrete. The design involves analyzing bending under uniform or concentrated loads, considering both transfer and service stages of prestressing.

What are the two stages of prestress discussed in the SNI code?

The two stages are Transfer and Service. Transfer occurs immediately after prestressing is applied, considering only the dead load, while Service considers both dead and live loads during the structure's use.

How are the allowable stresses for concrete defined in transfer and service stages?

For the transfer stage: compressive stress σ_cp = 0.6 f_ck and tensile stress σ_tt = 0.25 f_ck. For the service stage: compressive stress σ_cs = 0.45 f_ck and tensile stress σ_ts = 0.5 √f_ck.

How is the cross-sectional area of the beam calculated from the given dimensions?

The cross-sectional area A is calculated by multiplying the width and height of the beam: A = b × h = 0.4 m × 0.6 m = 0.24 m².

What is the formula used to calculate the bending stress in the beam due to prestress?

The bending stress formula is σ = -P/A ± P*e/Sx ∓ M/Sx, where P is the prestressing force, A is the cross-sectional area, e is the eccentricity of the tendon, Sx is the section modulus, and M is the bending moment due to applied loads.

How is the bending moment due to dead load and live load calculated for a simply supported beam?

The bending moment is calculated using M = (w * L²)/8 for dead load and M = (q * L²)/8 for live load, where w is the dead load per meter, q is the live load per meter, and L is the span length.

How do you determine the number of prestressing tendons required for a beam?

The number of tendons is determined using n_tendon = G_PR / (0.8 * f_ut), where G_PR is the required prestressing force and f_ut is the ultimate tensile strength of the tendon.

What is the significance of eccentricity 'e' in prestressed concrete design?

Eccentricity 'e' represents the distance from the centroidal axis of the beam to the line of action of the prestressing tendon. It creates a moment that counteracts bending due to external loads, reducing tensile stress at the bottom fibers of the beam.

Why is only the dead load considered during the transfer stage?

Only the dead load is considered during transfer because prestress is applied before the structure is exposed to live loads. This ensures that the prestress counteracts self-weight stress before additional loads are applied.

What checks are performed to ensure the beam's safety after applying prestress?

Checks include verifying that the total stress at the top and bottom fibers during both transfer and service stages is within allowable stress limits, and calculating the appropriate number of tendons to achieve the required prestressing force considering losses.

What adjustments can be made if the prestress force or concrete strength changes?

If prestress force or concrete strength changes, the number of tendons, tendon placement (eccentricity), or beam dimensions can be adjusted to ensure stresses remain within allowable limits and the design is safe and efficient.

How is the section modulus Sx of a rectangular beam calculated?

The section modulus Sx for a rectangular beam is calculated as Sx = (b * h²)/6, where b is the width and h is the height of the beam.