3 2 ANALIS DAN DESAIN LENTUR BALOK PERSEGI BERTULANGAN RANGKAP ANALISIS LENTUR

Summary

This video provides a comprehensive guide on analyzing double reinforced concrete beams. It explains the beam’s cross-section, reinforcement layout, and the assumptions of linear strain distribution. Viewers learn to calculate concrete compressive forces, tensile and compressive steel forces, and the nominal moment capacity, while considering whether the compressive reinforcement has yielded. The tutorial also covers checking reinforcement ratios to ensure tensile-controlled behavior, solving for the neutral axis, and applying stress block theory. Through detailed examples with step-by-step calculations, including real beam dimensions and reinforcement specifications, the video equips engineers and students with practical methods for designing and evaluating double reinforced beams efficiently.

Takeaways

• 😀 A double reinforced square beam consists of tensile reinforcement at the bottom and compressive reinforcement at the top, with a square concrete cross-section of width B and effective height D.
• 😀 The strain in concrete is assumed linear, with a maximum compressive strain of 0.003, and steel strain is denoted for tensile and compressive reinforcement.
• 😀 Concrete compressive force is calculated as Cc = 0.85 f'c * a * B, while tensile and compressive steel forces are T = As * Fy and Cs = As' * Fs, respectively.
• 😀 The nominal moment capacity of a double reinforced beam is the sum of the contributions from concrete compression and compressive steel: Mn = Cc * Z1 + Cs * Z2.
• 😀 To find the ultimate moment capacity, Mn is multiplied by the strength reduction factor, typically φ = 0.9.
• 😀 The condition of compressive reinforcement is checked using reinforcement ratios; if ρ_net = ρ - ρ' > k, the compressive steel has yielded, otherwise it has not.
• 😀 If compressive steel has yielded, the force balance is divided into concrete and steel contributions, and the concrete stress block height a is determined using a = As1 * Fy / (0.85 f'c * B).
• 😀 If compressive steel has not yielded, the stress in steel is calculated elastically, and a quadratic equation is used to solve for the neutral axis depth C, then a = β1 * C.
• 😀 The tensile-controlled condition is verified by ensuring the net reinforcement ratio is below ρ_max, which maintains ductile behavior of the beam.
• 😀 Example calculations demonstrate the full process, including determining ρ and ρ', checking yielding, calculating concrete block height, and computing Mn and Mu in kNm.
• 😀 Key formulas summarized include: Cc = 0.85 f'c * a * B, T = As * Fy, Cs = As' * Fy or Cs = Es * εs' (if not yielded), and Mn = Cc * (d - a/2) + Cs * (d - d').

Q & A

What is the main focus of the transcript?

The transcript focuses on analyzing a double reinforced square concrete beam, including calculating stress, strain, and the moment capacity of the beam.

What are the key components of a double reinforced beam cross-section?

The key components include the concrete section (width B and height D), tensile reinforcement at the bottom (A_s), compressive reinforcement near the top (A'_s) at a distance d' from the top fiber, and the neutral axis height C.

What assumptions are made about strain distribution in the beam?

The beam is assumed to have a linear strain distribution with the maximum concrete compressive fiber strain being 0.003, and the tensile and compressive steel strains denoted as ε_t and ε_s', respectively.

How is the concrete compressive force calculated in a double reinforced beam?

The concrete compressive force is calculated using the rectangular stress block assumption: C_c = 0.85 f'_c a B, where a is the height of the stress block determined by a = β_1 C.

How do you determine whether the compressive reinforcement has yielded?

By calculating the reinforcement ratio ρ_s = A'_s / (B*D) and comparing ρ_s with a limit value k. If ρ_s > k, the compressive reinforcement has yielded; if ρ_s < k, it has not yielded.

How is the nominal moment capacity of a double reinforced beam calculated?

The nominal moment capacity M_n is calculated as the sum of moments of concrete and compressive steel about the tensile steel: M_n = C_c Z_1 + C_s Z_2.

What is the procedure if the compressive reinforcement has not yielded?

If the compressive steel has not yielded, the compressive stress F_s' is calculated using elastic behavior (F_s' = E_s * strain), and the neutral axis height C is determined by solving the equilibrium equation: A_s F_y = C_c + C_s, often as a quadratic equation.

What is the role of the height of the concrete stress block 'a'?

The height 'a' represents the effective depth of the concrete compression zone and is used to calculate the concrete compressive force and its moment contribution. It is computed as a = β_1 C.

What are the steps to compute the ultimate moment M_u after finding the nominal moment M_n?

After determining M_n, multiply it by the strength reduction factor φ (typically 0.9 for tension-controlled sections) to get the ultimate moment: M_u = φ M_n.

How is the reinforcement ratio related to ductility of the beam?

The reinforcement ratio (ρ - ρ') must be smaller than the maximum limit ρ_max to ensure the section remains tensile-controlled, which provides ductile behavior and prevents sudden failure.

In the worked example, how was it determined that the compressive reinforcement yielded?

By calculating ρ - ρ' = 0.01567 and comparing it with the limit k = 0.001129. Since 0.01567 > 0.001129, the compressive reinforcement was considered yielded.

What is the importance of checking if the reinforcement is tensile-controlled?

Ensuring the section is tensile-controlled (ρ - ρ' < ρ_max) guarantees ductile failure and safety, as the tensile steel yields before concrete crushing, providing warning before collapse.