Reinforced CMU Lintel (TMS 402)
Strength design of a simply-supported, fully-grouted reinforced concrete-masonry lintel over an opening per TMS 402-16 (MSJC) Chapter 9. Computes the factored moment and shear from uniform gravity load, designs the bottom (tension) reinforcement using the masonry equivalent stress block, checks the masonry shear term with the M/(V·dv) factor, and verifies end bearing. Arching action is conservatively neglected (full load carried by the lintel). Fully customizable.
What this calculates
Actual lintel width, effective depth, and bottom steel area, factored midspan moment (Mu = wu·L²/8) and support shear, equivalent stress-block depth, nominal and design moment strength (φMn, φ = 0.90), maximum reinforcement ratio (ductility limit), masonry shear strength (Vnm) with the M/(V·dv) reduction and the upper cap, design shear strength (φVn, φ = 0.80), and demand-to-capacity ratios for flexure, ductility, shear, and bearing.
Inputs
Clear span of the opening
Nominal unit width (actual = nominal − 3/8 in)
Overall lintel depth (course count × 8 in nominal)
Length of bearing at each support
Specified compressive strength of masonry (TMS 402 §4)
Reinforcement yield strength (ASTM A615 Gr. 60)
Bottom (tension) bar designation
Number of bottom bars
Service dead line load (wall above + self-weight + dead reactions)
Service live line load (floor/roof reactions)
Outputs
Effective depth to bottom steel
Factored midspan moment wu·L²/8
Design moment strength with φ = 0.90
Design shear strength with φ = 0.80 (Vns = 0)
Flexural demand-to-capacity ratio — must be ≤ 1.0
Shear demand-to-capacity ratio — must be ≤ 1.0
Methodology
Per TMS 402-16 (MSJC) Strength Design, Chapter 9. Flexure uses the 0.80·f'm equivalent rectangular stress block per Section 9.3.2 with φ = 0.90. The maximum reinforcement ratio enforces ductility per Section 9.3.3.2 (α = 1.5 for beams). Masonry shear Vnm = (4.0 − 1.75·M/(V·dv))·An·√f'm per Section 9.3.4.1.2 (Eq. 9-21), capped by the 6→4·An·√f'm upper limit, with φ = 0.80. End bearing per Section 9.3.6. Load combination 1.2D + 1.6L per ASCE 7-22 Section 2.3.1. Excludes deflection serviceability and shear-reinforcement design.
Code References
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