Development of Reinforcing Bars

Reinforcement confinement factor

n_m = E_s/E_c is the modular ratio, with E_c = 120,000 w_c^2.0 f′_c^0.33; n in k_tr below is the number of developed bars.

With no confining reinforcement this reduces to λ_rc = d_b/c_b. Better confinement gives a smaller λ_rc and a shorter development length.

Using the figure

• Several splitting planes may be possible for one bar layout. Check each one; the case giving the largest λ_rc controls.
• c_b is measured to the center of the bar. This app forms c_b = min(cover + d_b/2, spacing/2) from the Bar Placement inputs, so cover is entered as clear cover to the bar surface.
• Count only the transverse legs that cross the plane you selected. Entering that count and the transverse bar size gives A_tr = n_legs × A_btr.
• n counts only bars being developed or spliced along that plane, not the other longitudinal bars.
• s is the center-to-center spacing of the transverse reinforcement measured along the developed length.

Transverse compression

Permanent compressive stress acting normal to the splitting plane adds to the confinement:

Enter f_c,transv = 0 when no permanent transverse compression acts across the plane. β_t applies only when confining reinforcement is present.

AASHTO LRFD Bridge Design Specifications, 10th Edition (2024), Article 5.10.8.2.1c and Figure C5.10.8.2.1c-1.