RC Beam Detailing from ETABS — Bars, Cutoffs and SMRF/IMRF Hoops, Drawn and Checked to ACI 318

Design checks

Calculation

1. 1Effective depth
   d = h - c_c - d_{hoop} - d_b/2
   d = 24.0 - 1.50 - 0.394 - 0.787/2
   d=21.71 in

   With the larger straight bar, Ø20.

2. 2Steel needed at support 1ACI318 10.5.1
   A_{s,req} = \max\!\left(A_{s,ETABS} + \tfrac{2}{3}A_l,\ A_{s,min},\ A_{s,seismic}\right)
   \text{top } 2.65,\quad \text{bottom } 1.00
   A_{s,req}=2.65 in²

   ETABS: top 2.05, bottom 0.40, Al 0.90 in².

3. 3Steel needed at mid-span 1ACI318 10.5.1
   A_{s,req} = \max\!\left(A_{s,ETABS} + \tfrac{2}{3}A_l,\ A_{s,min},\ A_{s,seismic}\right)
   \text{top } 0.87,\quad \text{bottom } 1.40
   A_{s,req}=1.40 in²

   ETABS: top 0.30, bottom 1.20, Al 0.30 in². Top set by As,min (§10.5.1).

4. 4Steel needed at support 2ACI318 10.5.1
   A_{s,req} = \max\!\left(A_{s,ETABS} + \tfrac{2}{3}A_l,\ A_{s,min},\ A_{s,seismic}\right)
   \text{top } 2.33,\quad \text{bottom } 0.98
   A_{s,req}=2.33 in²

   ETABS: top 1.80, bottom 0.45, Al 0.80 in².

5. 5Continuous barsACI318 21.5.2.1
   A_s = \textstyle\sum n\,\pi d_b^2/4
   \text{top } 3-Ø16 = 0.93\ \text{in}^2,\quad \text{bottom } 3-Ø20 = 1.46\ \text{in}^2
   A_{s,top}=0.93 in²

   Top: the least top requirement along the beam (and ¼ or ⅕ of the largest at a face); bottom: the largest mid-span requirement and As,min — both at least 2 bars.

6. 6Extra top 1-Ø20 + 4-Ø16 at support 1 — cut-off from the moment diagramACI318 12.10.3
   L = \max\!\left(x_{\phi M_n = M_u} + \max(d, 12d_b),\ \ell_d\right)
   L = \max(86.2,\ 37.3) \to 87\ \text{in}
   L=87 in

   Continuing bars 0.93 in² carry φMn 88.5 kip·ft; into span 1: φMn of the continuing bars met at 64.5 in from the face (Mpr + gravity); Vu 35.0 ≤ ⅔φVn 39.1 kip (§12.10.5). + max(d, 12db) = 21.7 in; ℓd 37.3 in (SMF §21.7.5 (3.25·ldh)). moment diagram + d or 12db (§12.10.3) governs: 7'-3" past the face.

7. 7Extra top 1-Ø20 at support 2 — cut-off from the moment diagramACI318 12.10.3
   L = \max\!\left(x_{\phi M_n = M_u} + \max(d, 12d_b),\ \ell_d\right)
   L = \max(81.1,\ 37.3) \to 84\ \text{in}
   L=84 in

   Continuing bars 0.93 in² carry φMn 88.5 kip·ft; into span 2: φMn of the continuing bars met at 59.4 in from the face (Mpr + gravity); Vu 33.4 ≤ ⅔φVn 39.1 kip (§12.10.5); back into span 1: φMn of the continuing bars met at 58.7 in from the face (Mpr + gravity); Vu 34.4 ≤ ⅔φVn 39.1 kip (§12.10.5). + max(d, 12db) = 21.7 in; ℓd 37.3 in (SMF §21.7.5 (3.25·ldh)). moment diagram + d or 12db (§12.10.3) governs: 7'-0" past the face.

8. 8Extra top 2-Ø20 at support 2 — cut-off from the moment diagramACI318 12.10.3
   L = \max\!\left(x_{\phi M_n = M_u} + \max(d, 12d_b),\ \ell_d\right)
   L = \max(67.2,\ 37.3) \to 69\ \text{in}
   L=69 in

   Continuing bars 1.42 in² carry φMn 132.2 kip·ft; into span 2: φMn of the continuing bars met at 45.5 in from the face (Mpr + gravity); Vu 36.5 ≤ ⅔φVn 39.1 kip (§12.10.5); back into span 1: φMn of the continuing bars met at 44.9 in from the face (Mpr + gravity); Vu 36.7 ≤ ⅔φVn 39.1 kip (§12.10.5). + max(d, 12db) = 21.7 in; ℓd 37.3 in (SMF §21.7.5 (3.25·ldh)). moment diagram + d or 12db (§12.10.3) governs: 5'-9" past the face.

9. 9Probable-moment shear VeACI318 21.5.2.1
   V_e = \dfrac{M_{pr,top} + M_{pr,bot}}{\ell_n} + V_g
   V_e = \dfrac{321.2 + 186.0}{14.50} + 18.0
   V_e=53.0 kip

   M from As 2.67 (top) and 1.46 in² (bottom) at 1.25·fy; Vg as read or typed.

10. 10Hoop spacing from VeACI318 11.2.1 / Eq. 11-3
    s = \dfrac{A_v f_{yt} d}{V_e/\phi - \phi V_c}
    s = \dfrac{0.243 \cdot 60 \cdot 21.71}{70.6}
    s=4.5 in

    φVc = 0 within ℓo (§21.5.4.2).

11. 11Hoops within 2h of each faceACI318 21.5.2.1
    s \le \min(s_{code}, s_{demand}, s_{V_e}, s_{torsion})
    \text{Ø10, 2 legs @ 3 in, governed by \S 21.5.3}
    s=3 in

    Zone 4'-0"; 2 legs: a closed hoop.

12. 12Stirrups betweenACI318 21.5.2.1
    s \le \min(d/2, s_{demand}, s_{torsion})
    \text{Ø10, 2 legs @ 7 in, governed by torsion (\S 11.6.6.1)}
    s=7 in

    Zone 8'-0"; 2 legs: a closed hoop.

13. 13Hook of the continuous top bars at the end columnACI318 12.5
    \ell_{dh} = \dfrac{f_y d_b}{65\sqrt{f'_c}} \ge 8d_b,\ 6\text{ in}
    \ell_{dh}(\text{Ø16})
    \ell_{dh}=9.2 in

Assumptions

• The steel each location needs is ETABS's concrete beam design (top and bottom As, Av/s, Al, At/s), the largest over the outer tenth of each span at a support and over the middle third at mid-span, plus (2/3)·Al on each of top and bottom as the owner's Beam_DCR workbook takes it.
• SMF: As,min (§10.5.1) on both faces everywhere (§21.5.2.1); the moment ratios (§21.5.2.2: M+ ≥ ½ M− at a face, any section ≥ ¼ of the largest) through Mn, not the steel area.
• Bars of the sizes ticked (Ø16, Ø20, Ø25, Ø28, Ø32), mirror-symmetric (two of one size, then a centre bar or a ring of another size), the narrowest web setting how many fit a layer — by CRSI's table of the most bars in a single layer (overall diameters, the corner bars in the hoop's bends, clear space ≥ 1 in, db and 4/3 × ¾ in aggregate), the size giving the fewest layers chosen first, extras filling the continuous bars' layer before the next; extra bars cut where the moment diagram lets them go, as PCA Notes' Example 29.2: past the point where φMn of the continuing bars meets Mu by max(d, 12db) (§12.10.3), at least ℓd past the face (§12.10.4), the farthest third of a support's top steel past the inflection point by d, 12db or ℓn/16 (§12.12.3), and §12.10.5 checked at the cut (Vu ≤ ⅔φVn, else on into compression); the diagram the envelope of ETABS's M3 (or the moment of the steel it asked for) and, in an SMF, the probable moments at the faces with the gravity load (w = 2Vg/ℓn, ¾ of it for the negative moments); rounded up to 3 in. The drawing measures them from the column faces.
• Hoops Ø10, 2 legs or more, each zone as it needs: within 2h of an SMF's face every corner and alternate bar held, none more than 6 in clear from a held one (§21.5.3.3, §7.10.5.3); a crosstie added where ETABS's demand or Ve would close the hoops below 4 in (torsion on the two outer legs only). Spacing: within 2h of each face at the least of the code limit, ETABS's demand, the capacity-design shear and the torsion limit; between, d/2 or less.