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Consider a beam of width 300 mm, effective depth 450 mm, VuVu = 280 kN, M1M1 = 200 kNm, τbdτbd = 1.2 N/mm2. The maximum diameter (in mm) of the deformed bar going into the support of simply supported beam. (Assume end confinement without any anchorage length). Take Fe 415.
  • a)
    19
  • b)
    20
Correct answer is between '19,20'. Can you explain this answer?
Most Upvoted Answer
Consider a beam of width 300 mm, effective depth 450 mm, VuVu = 280 k...
Calculation of Maximum Diameter of Deformed Bar

Given data:
Width of beam (b) = 300 mm
Effective depth of beam (d) = 450 mm
Shear force (Vu) = 280 kN
Bending moment at support (M1) = 200 kNm
Design shear strength of concrete (τbd) = 1.2 N/mm2
Grade of steel (Fe) = 415

Step 1: Calculation of Shear Stress
The shear stress (τ) developed in the beam can be calculated as:
τ = Vu / (b × d)
τ = 280000 / (300 × 450)
τ = 2.96 N/mm2

Step 2: Calculation of Lever Arm
The lever arm (a) can be calculated as:
a = d – (0.5 × effective depth of compression zone)
a = 450 – (0.5 × 0.87 × 450)
a = 256.13 mm

Step 3: Calculation of Bending Stress
The bending stress (σ) developed in the beam can be calculated as:
σ = M1 / (0.87 × fyk × a)
where fyk is the characteristic strength of steel, which can be calculated as:
fyk = 0.87 × fy
where fy is the yield strength of steel, which is 415 N/mm2 for Fe 415.

fyk = 0.87 × 415
fyk = 361.05 N/mm2

Now, substituting the values in the equation for σ, we get:
σ = 200000 / (0.87 × 361.05 × 256.13)
σ = 0.972 N/mm2

Step 4: Calculation of Maximum Diameter of Deformed Bar
The maximum diameter (dmax) of the deformed bar can be calculated using the following equation:
dmax = 0.95 × a × √(τbd / σ)
where 0.95 is the reduction factor for confinement, and τbd is the design shear strength of concrete.

Substituting the values, we get:
dmax = 0.95 × 256.13 × √(1.2 / 0.972)
dmax = 19.33 mm (approx.)

Therefore, the maximum diameter of the deformed bar that can be used at the support of the simply supported beam is 19-20 mm (rounded off).
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Community Answer
Consider a beam of width 300 mm, effective depth 450 mm, VuVu = 280 k...
Maximum diameter = 19.75mm
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Consider a beam of width 300 mm, effective depth 450 mm, VuVu = 280 kN, M1M1 = 200 kNm, τbdτbd = 1.2 N/mm2. The maximum diameter (in mm) of the deformed bar going into the support of simply supported beam. (Assume end confinement without any anchorage length). Take Fe 415.a)19b)20Correct answer is between '19,20'. Can you explain this answer?
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