Tools › Civil and Geotechnical › Timber and Masonry › Masonry Wall and Pier › Example
TM 5-809-3 wall design example 1: 12 in CMU wall under wind and an eccentric axial load, one #6 bar at 24 in
| Tool | Masonry Wall and Pier |
| Source | Departments of the Army, the Navy and the Air Force (1992). Masonry Structural Design for Buildings. TM 5-809-3 / NAVFAC DM-2.9 / AFM 88-3, Chap. 3, Washington, DC. Chapter 6, design example 1 (pp. 6-4 to 6-7); chapter 5, eqs 5-9 to 5-20 and 5-24 / 5-25, Tables 5-1, 5-3, 5-5 and 5-7. |
| Level | Undergraduate |
Problem
A 12 in hollow concrete-masonry loadbearing wall 24 ft high carries 1,500 lb/ft at an eccentricity of t/2 = 5.8125 in and a 25 lb/ft² wind load whose moment adds to the eccentric moment; f′_m = 1,350 lb/in² (type S mortar), F_s = 24,000 lb/in², E_m = 1,000 f′_m, one #6 bar (0.44 in²) per cell at 24 in. Find the reaction, the location and value of the maximum moment, the transformed-section coefficients, the masonry and steel resisting moments (rectangular and T-section), the axial stress and its allowable with the slenderness factor, and check the unity equation with the one-third increase for wind.
Inputs to Enter
- Element: reinforced wall; masonry hollow units type M or S (f′_m 1,350 lb/in²), E_m rule 1,000 f′_m, F_s 24,000, E_s 29,000,000 lb/in², wind or seismic checked
- 12 in CMU (t 11.625, t_s 1.5, d_1 5.81, b_w 7.5 in), one bar per cell, spacing 24 in, A_s 0.44 in², h 24 ft, w 25 lb/ft², P 1,500 lb/ft, e 5.8125 in, moments additive, A_e and wall weight blank (Table 5-3: 68 in²/ft, Table 5-5: 102 lb/ft²), section rule automatic
Answers
- R_a = wh/2 + Pe/h = 300.0 + 30.3 = 330.3 lb/ft; x = h/2 + Pe/(wh) = 13.2 ft; M_max = 2,182 ft-lb/ft, design moment 4,364 ft-lb per 24 in (manual: 330.3, 13.2, 2,182, 4,364)
- n = 21.5, p = 0.0032, np = 0.0678, k = 0.307, j = 0.898, kd = 1.78 in beyond the 1.5 in face shell (manual: 0.308, 0.897, 1.79), so the T-section governs: k_T = 0.310, j_T = 0.902, M_rmT = 4,129 ft-lb, M_rsT = 4,610 ft-lb (manual: 0.312, 0.902, 4,147 and 4,611; Table B-4 4,147 / 4,603); rectangular M_rm 4,181 (manual 4,196 with its rounded k, j)
- f_a = [1,500 + 102 (24 − 13.2)]/68 = 38.2 lb/in², R = 1 − (12 × 24/(40 × 12))³ = 0.784, F_a = 0.20 × 1,350 × 0.784 = 211.7 lb/in² (manual 38.3, 212.0)
- Unity with the one-third increase: 38.2/281.5 + 4,364/5,491 = 0.136 + 0.795 = 0.930 ≤ 1 (manual 0.14 + 0.79 = 0.93); margin +0.07; steel ratio 0.633 (margin +0.58); out-of-plane shear f_v = R_a s/(b_w d) = 15.2 lb/in² against 48.9
Notes
The tool's default inputs are this example; press Submit. The manual's numbers are reproduced to its rounding (it rounds np to 0.0688 and k to 0.308); every value is checked by test_masonry_wall_pier.php (621 checks) against the manual's printed examples 6-1, 6-3, 7-1, 7-2, 8-1, 8-2, 8-3 and 9-6, its Tables 5-1 to 5-5 and 5-12 to 5-14, and the numpy script in References/Masonry/checks/. The manual applies the 1.33 increase to the resisting moments and F_a; the tool does the same so the unity limit stays 1.0.