A 6m simply supported beam carries a uniform live load of 20kN/m and a dead load of 12kN/m (including its own weight).Use f'c=28MPa, fy=345MPa, b=d/2. Choose appropriate bar diameters and check for shear.
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Problem 2 (Design Problem):
Design the beam shown to carry a service live load of 20kN/m and a dead load of 15kN/m (including its own weight). Use f'c=21MPa, fy=276MPa, b=d/2. The beam is to be reinforced for tension only. Check also for shear.
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CE Board Nov. 2021
A beam has reinforcement at the top of 3 – 28 mm ∅ bars and at the bottom 5 – 28 mm ∅ bars. There are 3 legs of vertical stirrups as shown. The beam section has h1 = 110 mm (flange) and h2 = 490 mm (stem), bw = 350 mm, total h = 600 mm. Concrete cover to centroid of reinforcement = 70 mm. Stirrups: 10 mm ∅, spacing s = 100 mm. fc' = 27.5 MPa, fy = 415 MPa, fyv = 225 MPa.
Determine the shear strength of the stirrups, Vs.
Determine the shear strength of the concrete, Vc.
Determine the maximum allowable spacing of the stirrups.
#1 — Shear Strength of Stirrups (Vs)
Three legs of 10 mm ∅ stirrups; effective depth = h − cover to centroid:
A column 600 mm in diameter is reinforced with 8 – 25 mm ∅ bars and 12 mm ∅ spirals spaced at 100 mm on centers. φ = 0.75, fy = 413 MPa (main bars), fyt = 275 MPa (spirals), fc' = 30 MPa.
What is the nominal shear strength provided by the concrete?
What is the nominal shear strength provided by the shear reinforcement?
Find the shear stress in the column if Vu = 800 kN.
#1 — Nominal Shear Strength by Concrete (Vc)
For solid circular sections (§22.5.2.2): d = 0.8D = 0.8(600) = 480 mm, bw = D = 600 mm:
From the figure: h1 = 125 mm, h2 = 475 mm (total h = 600 mm). Bottom steel: 8 – 28 mm ∅ bars arranged in 2 layers of 4, with a clear distance of 55 mm between rows. Top steel: 4 – 28 mm ∅ bars. fc' = 28 MPa, fy = 415 MPa, fyt = 275 MPa. Tie diameter = 12 mm, φ = 0.75, clear concrete cover = 40 mm, maximum aggregate size = 20 mm.
Find the minimum width of beam "b" required to satisfy cover requirements.
Find the minimum width "b" for Vu = 600 kN with 12 mm ∅ ties at s = 50 mm.
If Vu = 450 kN with 12 mm ∅ ties at s = 70 mm, find the required minimum "b".
#1 — Minimum Width for Cover Requirements
Governing clear spacing (§25.2.1) — greatest of 25 mm, db = 28 mm, (4/3)(20) = 26.67 mm → 28 mm governs.
Beam BE is simply supported at B and E. S = 2.6 m (beam spacing), L = 5.3 m span. Slab thickness t = 100 mm. Beam: b = 250 mm, H = 400 mm. Effective cover to centroid of steel = 75 mm. fc' = 20.7 MPa, fy = 415 MPa, fyv = 275 MPa. Unit weight of concrete = 23.6 kN/m³. Superimposed DL = 2.6 kPa (slab weight NOT included). Live load = 3.6 kPa. Use U = 1.2DL + 1.6LL.
Which of the following gives the span moment (kN·m) at beam BE?
Which of the following gives the maximum shear force Vu (kN) at the critical section at support B?
Which of the following gives the nominal shear strength (kN) provided by the concrete?
A two-span beam subjected to shear and flexure only is reinforced as follows. At supports: 5 – 25 mm ∅ top bars, 3 – 25 mm ∅ bottom bars. At midspan: 3 – 25 mm ∅ top bars, 3 – 25 mm ∅ bottom bars. Lateral ties: 10 mm ∅. fc' = 27.5 MPa, fy = 415 MPa, fyt = 275 MPa. Beam: b × h = 350 × 450 mm, d = 375 mm, slab thickness = 100 mm. Use U = 1.2D + 1.6L.
What is the nominal shear capacity Vn (kN) at the supports if ties are 3-legged at s = 100 mm?
At midspan where shear is minimum, what is the theoretical maximum spacing of 2-leg lateral ties?
Calculate the ultimate moment capacity at the supports in kN·m.
Use the lesser (more restrictive): S = 352.6 mm → round down to:
\[ \boxed{S_{\max} = 350 \text{ mm}} \]
This is the theoretical maximum from Av,min requirements. In practice, the code maximum spacing of d/2 = 187.5 mm (Table 409.7.6.2.2) applies when stirrups are required, and would govern over 350 mm.
#3 — Ultimate Moment Capacity at Supports
As = 5 × π/4(25)² = 2454.37 mm² (5 top bars), b = 350 mm, d = 375 mm, β1 = 0.85
