Internal Bracing Design Program Background Information 2016 by International Masonry Institute All rights reserved. This program is intended as a preliminary design tool for design professionals who are experienced and competent in masonry design. This program is not intended to replace sound engineering knowledge, experience, and judgment. Users of this program must determine the validity of the results. The International Masonry Institute assumes no responsibility for the use or application of this program. This document provides the background to the Internal Bracing Design Program. The values shown may not be identical to the ones in the Standard Practice for Bracing Masonry Walls Under Construction (Council for Masonry Wall Bracing, 2012) due to rounding or because the Practice values are calculated from the 2008 code and the software offers updated code options. The same engineering principals were used as with the Standard Practice, and all values meet the intent of Standard Practice.
This program provides the maximum height of unbraced wall for the initial period, an unreinforced wall in the intermediate period (both bonded and unbonded), and a reinforced wall in the intermediate period. The program is based on allowable stress design. Program inputs Code o o 2015 IBC (2013 TMS402/602) 2012 IBC (2011 TMS402/602) Masonry type: o Lightweight, medium weight, or normal weight CMU o Solid or hollow units o Nominal thickness: 4, 6, 8, 10, 12, 14, or 16 inch o Specified compressive strength, f m. This can be automatically calculated Mortar type: Type N or S; masonry cement or Portland cement/mortar cement Wall properties: actual thickness, net area, section modulus, and weight. All of these can be automatically calculated, or manually input for special cases. Construction: grout spacing, rebar spacing (none or same as grout spacing), rebar size (#3 through #9) Footing dimensions: depth and width of footing Program outputs: Maximum unbraced height for initial period Maximum unbraced height for intermediate period for unreinforced, unbonded walls Maximum unbraced height for intermediate period for unreinforced, bonded walls Maximum unbraced height for intermediate period for reinforced walls o Required lap lengths for 12 hours and 24 hours after placement of grout Minimum and maximum soil bearing pressures; these bearing pressures will need to be compared to allowable bearing pressures for the site. The following sections detail the calculations that are used in the program.
Initial Period Requirements: The lowest unit weight of block is used for each weight category of blocks. This will be conservative. The wind pressure is determined as 0.00256vv 2 where v = 22 mph. Pressure is 1.239 psf A factor of safety of 1.5 is used. Determine height. h = (wwwwwwww wwwwwwwwhtt)(aaaaaaaaaaaa tthiiiiiiiiiiiiii) (wwwwwwww pppppppppppppppp)(ffffffffffff oooo SSSSSSSSSSSS) The height is converted to an 8 inch module. If the height is less than 8 ft, an 8 ft height is output, based on OSHA allowing up to 8 ft without bracing. The maximum height is limited to 35 ft. Note that due to the 8 inch module, the actual maximum output by the program is 34 ft-8in. The program distinguishes between solid units and fully grouted units. This difference can be substantial, particularly for smaller thickness units and lightweight units. For example, 6 inch lightweight solid units weigh 46 psf, and have a maximum initial unbraced height of 11-4. Fully grouted lightweight 6 inch hollow units weigh 56 psf, and have a maximum initial unbraced height of 14-0.
Unreinforced Design A factor of 0.67 is applied to the allowable flexural tensile stress to account for the early age. The design wind speed is 40 mph; pressure is 4.096 psf. The allowable flexural tension stress will typically control. The height of wall is determined using the load combination 0.6D+W. The wind pressure determined is an allowable stress level wind pressure, so there is no 0.6 factor on the wind load, as would be used if a strength level wind load was used. The maximum wall height by solving the following quadratic equation: pp 2SS nn h 2 0.6ww wwwwwwww AA nn h 0.67FF tt = 0 where p is the wind pressure, S n is the net section modulus, w wall is the wall weight, A n is the net area, and F t is the allowable flexural tensile stress. For an unbonded wall, F t is set = 0. The program then checks compression using the unity equation. If compression does control, the height of the wall is incrementally decreased by one block at a time until compression is satisfied. The steps to check for compression controlling are: 1. Determine the axial stress as f a = P/A n and the bending stress as f b = 12M/S n. 2. Determine the allowable flexural compressive stress as F b = (1/3)f I, where f I = ½ f m. 3. Determine the radius of gyration as rr = SS nntt 2AA nn, where S n is the section modulus, t is the actual thickness, and A n is the area. 4. Determine h/r, where h is the height of the wall. 5. If h/r is 99, then FF aa = 1 ff 4 1 h 140rr 2. If h/r >99, then FF aa = 1 ff 4 70 (h/rr) 2. 6. Calculate the quantity of ff aa + ff bb. If this quantity is 1, then OK. If it is greater than 1, then FF aa FF bb reduce the height of the wall by one block and recheck. Verification Example, Bonded: Given 12 inch lightweight hollow, ungrouted block with Type N masonry cement mortar. The wall weight is 35 psf. The program gives a maximum unbraced height of 8-8. Use the 2012 IBC. Check this result. Wall weight: PP = ww wwwwwwww h = 35pppppp(8.67) = 303 llll Factored axial load: 0.6PP = 0.6 303 llll llll = 182 Axial stress: ff aa = PP = 182llll/ = 6.1 pppppp AA nn 30iinn 2 / Moment from wind: MM = pph2 = 4.1pppppp(8.67)2 = 153.8 llll 2 2
Bending stress: ff bb = MM = 153.8llll 12 iiii SS nn 139.6 iinn3 = 13.2pppppp Tension stress: ff tt = ff bb ff aa = 13.2pppppp 6.1pppppp = 7.2 pppppp Allowable tension stress: FF tt = 0.67(12pppppp) = 8 pppppp Check tension: 7.2 pppppp 8 pppppp OK Allowable masonry compression stress: FF bb = 1 ff 3 ii = 1 3 1 1350pppppp = 225pppppp 2 Radius of gyration: rr = 139.6iinn3 (11.62iiii) 2 30 iinn2 Slenderness ratio: h rr = 8.67 12iiii 5.20iiii = 20.0 = 5.20iiii Allowable axial stress: FF aa = 1 ff 4 ii 1 h 140rr 2 = 1 4 1 1350pppppp 1 20.0 2 140 2 = 165.3pppppp Check unity equation: ff aa + ff bb = 6.1pppppp + 13.2pppppp = 0.095 1.0 OK FF aa FF bb 165.3pppppp 225pppppp Verification Example, Unbonded: Rework the problem, but with unbonded masonry. The program gives a maximum unbraced height of 3-4. Check this result. Wall weight: PP = ww wwwwwwww h = 35pppppp(3.33) = 117 llll Factored axial load: 0.6PP = 0.6 117 llll llll = 70 Axial stress: ff aa = PP = 70llll/ = 2.3 pppppp AA nn 30iinn 2 / Moment from wind: MM = pph2 = 4.1pppppp(3.33)2 = 22.8 llll 2 2 Bending stress: ff bb = MM = 22.8llll 12 iiii SS nn 139.6 iinn3 = 2.0pppppp Tension stress: ff tt = ff bb ff aa = 2.0pppppp 2.3pppppp = 0.3 pppppp Check tension: -0.3 pppppp 0 pppppp OK Compression is OK by inspection.
Bearing Pressure: The density of the concrete footing is assumed to be 145 lb/ft 3. Define d f as the depth of the footing and w f as the width of the footing. The steps to determine the footing pressures are: 1. AAAAAAAAAA ff = ww wwwwwwww h wwwwwwww + γγ ff dd ff ww ff 2. σσ aa = AAAAAAAAAA ff ll ff ww ff 3. MMMMMMMMMMMM = pp wwwwwwww h wwwwwwww dd ff + h wwwwwwww 2 4. SS = 12iiii ww ff 2 6 where σσ aa is the axial stress and l f is the length of the footing (12in/ft) where S is the section modulus 5. σσ bb = MMMMMMMMMMMM where σσ SS bb is the bending stress 6. MMMMMMMMMMMMMM bbbbbbbbbbbbbb sstttttttttt = σσ aa σσ bb 7. MMMMMMMMMMMMMM bbbbbbbbbbbbbb ssssssssssss = σσ aa + σσ bb Verification Example, Bonded: Given 12 inch lightweight hollow, ungrouted block with Type N masonry cement mortar. The wall weight is 35 psf. The program gives a maximum unbraced height of 8-8, which was previously verified. The footing dimensions are 24 inches wide x 12 inches deep. Check the program results. 1. AAAAAAAAAA ff = ww wwwwwwww h wwwwwwww + γγ ff dd ff ww ff = 35pppppp(8.67) + 1fftt2 llll (12iiii)(24iiii) 3 2 = 593 145 llll fftt 2. σσ aa = 144iinn AAAAAAAAAA ff = 593 llll iinn2 144 ww ff ll ff 24iiii 12 iiii 3. MMMMMMMMMMMM = pp wwwwwwww h wwwwwwww dd ff + h wwwwwwww 2 4. SS = 12iiii ww ff 2 6 5. σσ bb = MMMMMMMMMMMM SS fftt 2 = 297pppppp = 12iiii (24iiii)2 = 1152 iinn3 fftt3 = 0.667 6 = 189.3llll 0.667 fftt3 = 284pppppp 8.67 = 4.1pppppp(8.67) 1 + = 189.3 llll 6. MMMMMMMMMMMMMM bbbbbbbbbbbbbb ssssssssssss = σσ aa σσ bb = 297pppppp 284pppppp = 13pppppp 7. MMMMMMMMMMMMMM bbbbbbbbbbbbbb ssssssssssss = σσ aa + σσ bb = 297pppppp + 284pppppp = 581pppppp These results agree with the program. The bearing pressures would need to be compared to the allowable soil bearing pressures for the site. 2
Reinforced wall design: For a given section (block size and density, f m, reinforcing size and spacing), the maximum unbraced height is determined in an iterative fashion. The height of the wall is increased incrementally by one block until the applied bending moment exceeds the allowable bending moment. The allowable moment is determined based on the axial load. The axial load is 0.6 times the wall weight (load factor of 0.6). There are four cases for the allowable moment, as shown below. In each case, a quadratic equation is solved for kd. Once kd is known, an allowable moment is determined. The calculations are based on the initial compressive strength ff ii = 1 ff 2. 1. Allowable tension stress, F s, controls. Neutral axis in face shell. εε ss = FF ss kkkk εε dd kkkk ss εε = ff = εε EE CC = 1 kkkk(bb)ff 2 TT = FF ss AA ss CC TT = PP 1 bb FF ss EE 2 EE (kkkk) 2 + (AA ss FF ss + PP)kkkk (AA ss FF ss + PP)dd = 0 ss MM aaaaaa = CC dd kkkk 3 2. Allowable tension stress, F s, controls. Neutral axis web. εε ss = FF ss kkkk εε dd kkkk ss εε = ff = εε EE εε 1 = kkkk tt dd kkkk εε ss ff 1 = εε 1 EE CC, = 1 2 tt (bb)(ff + ff 1 ) CC,wwwwww = 1 kkkk tt 2 (bb ww )(ff 1 ) TT = FF ss AA ss 1 bb FF ss 2 ww EE (kkkk) 2 + (bb bb ww ) FF ss EE tt + AA ss FF ss PP kkkk 1 2 (bb bb ww ) FF ss EE tt xx = ff + 2ff 1 tt ff + ff 1 3 MM aaaaaa = CC, dd xx + CC,wwwwww dd tt kkkk tt 3 3. Allowable masonry compression stress, F b, controls. Neutral axis in face shell. εε = FF bb EE εε ss = dd kkkk εε kkkk 2 AA ss FF ss dd = 0
ff ss = εε ss CC = 1 kkkk(bb)ff 2 bb TT = ff ss AA ss CC TT = PP 1 bbff 2 bb (kkkk)2 FF + AA bb FF ss EE PP kkkk AA bb ss EE dd = 0 MM aaaaaa = CC dd kkkk 3 4. Allowable masonry compression stress, F b, controls. Neutral axis in web. εε = FF bb EE εε ss = dd kkkk εε kkkk ff ss = εε ss εε 1 = kkkk tt εε kkkk ff 1 = εε 1 EE CC, = 1 tt 2 (bb)(ff + ff 1 ) CC,wwwwww = 1 kkkk tt 2 (bb ww )(ff 1 ) TT = ff ss AA ss 1 bb 2 wwff bb (kkkk) 2 FF + (bb bb ww )FF bb tt + AA bb ss EE PP kkkk 1 (bb bb 2 ww )FF bbtt 2 FF AA bb ss EE dd = 0 xx = ff + 2ff 1 tt ff + ff 1 3 MM aaaaaa = CC, dd xx + CC,wwwwww dd tt kkkk tt 3 The splice lengths are determined as follows: 12 hours after placement of grout: 0.0027dd bb FF ss but not less than 16 inches 24 hours after placement of grout: 0.002dd bb FF ss but not less than 12 inches
Reinforced Masonry Wall Example 1: This is Example 1 from the Internal Bracing Design Guide for Masonry Walls under Construction (IMI, 2013). The internal bracing is designed for a 28-0 tall, 12 inch CMU wall with #6 bars at 40 inch on center, and Type S mortar. The 2009 IBC is used. The above values are input into the program; lightweight units are used and an f m of 1500 psi. The program gives a maximum unbraced height of 24-8. Thus, the internal bracing is not adequate, which is consistent with what is determined in the guide. The guide suggests increasing f m to 2500 psi. When this is done in the program (uncheck the automatic box for f m, and enter 2500 psi), the maximum height is 29-4, and the internal bracing is adequate. By trial and error, it also determined that an f m of 2100 psi will work. Another option would be to use the 2012 IBC (if allowed by the local building official). With the higher allowable stresses, the maximum unbraced height is 28-0 with an f m of 1500 psi. However, with the higher allowable stress, a splice length of 48 inches is required at 24 hours instead of 36 inches. Reinforced Masonry Wall Example 2: This is Example 2 from the Internal Bracing Design Guide for Masonry Walls under Construction (IMI, 2013). The internal bracing is designed for a 20-0 tall, 8 inch CMU wall with #5 bars at 32 inch on center, and Type S mortar. The 2009 IBC is used. The above values are input into the program; lightweight units are used and an f m of 1500 psi. The program gives a maximum unbraced height of 17-4. Thus, the internal bracing is not adequate, which is consistent with what is determined in the guide. The guide suggests increasing f m to 2500 psi. When this is done in the program (uncheck the automatic box for f m, and enter 2500 psi), the maximum height is 20-8, and the internal bracing is adequate. By trial and error, it also determined that an f m of 2250 psi will work. Another option would be to use the 2012 IBC (if allowed by the local building official). With the higher allowable stresses, the maximum unbraced height is 20-0 with an f m of 1500 psi. However, with the higher allowable stress, a splice length of 40 inches is required at 24 hours instead of 30 inches.