Shop — CMU OOP Checks (Typical Wall + OH Door Jamb)

1. References & Design Basis

Governing out-of-plane pressure used in calc packet: $p = 33 \ \mathrm{psf}$ (controls over wind $25 \ \mathrm{psf}$).
Wall height / unbraced height used: $L = 26.5 \ \mathrm{ft}$ (foundation to roof diaphragm / bond beam).
CMU: 8" nominal, 7.625" actual thickness; $f'_m = 2000 \ \mathrm{psi}$; reinforcing steel $F_y = 60 \ \mathrm{ksi}$.

Grouting basis (S-301 intent): Typical CMU walls are partially grouted UNO; grout all cells containing reinforcing/embeds/bolts. Walls are not solid grouted unless specifically called out. The typical wall check below uses tributary width equal to the vertical bar spacing. Openings (e.g., OH door jambs) are evaluated separately as boundary elements using scheduled jamb piers.

2. Typical Wall (No Openings) — Partially Grouted MW8 OOP Check

Purpose: Address whether a typical MW8 partially grouted wall region (away from openings) is adequate for the governing OOP pressure envelope.

Item	Value	Comment
Wall type	MW8 (8") — partially grouted UNO	Typical construction; grout only reinforced/anchored cells.
Vertical reinforcement (typical)	(1) #5 @ 32" o.c.	Typical vertical bar spacing governs tributary width for OOP strip check.
OOP pressure	$p = 33\ \mathrm{psf}$	From governing envelope used in calc packet.
Unbraced height	$L = 26.5\ \mathrm{ft}$	Assume lateral support at top (roof diaphragm/bond beam) and bottom (foundation).

2.1 Demand on Typical Wall Strip

Step	Expression	Result	Comment
2.1.1	Tributary width (bar spacing): $b_{trib} = 32"/12$	$b_{trib} = 2.667\ \mathrm{ft}$	Typical strip away from openings.
2.1.2	Line load: $w = p\,b_{trib}$	$w = 33(2.667)=88\ \mathrm{plf}$	Uniform line load on typical strip.
2.1.3	Moment demand (simple span): $M_u=\dfrac{wL^2}{8}$	$$M_u=\frac{(88)(26.5^2)}{8}=\frac{(88)(702.25)}{8}=7.72\ \mathrm{k\!-\!ft}$$	Assumes top/bottom out-of-plane lateral support.

2.2 Capacity of Typical Partially-Grouted Strip (Flexure about Thickness)

Flexure is about wall thickness $t$. Use a reviewer-facing rectangular stress block check on the tributary strip width $b=32$ in with one #5 bar. (KaTeX note: bar marks shown as text to avoid rendering issues.)

Item	Expression	Result	Comment
Geometry	$t=7.625\ \mathrm{in},\ b=32\ \mathrm{in}$	—	$t$ controls OOP bending; $b$ is tributary strip width along wall.
Steel area	$A_s=A_b$ (one bar)	$A_s=0.31\ \mathrm{in^2}$	One #5 bar (area $0.31\ \mathrm{in^2}$).
Effective depth	Assume bar centroid $\approx 1.875$ in from tension face (typ.)	$$d=t-1.875=7.625-1.875=5.75\ \mathrm{in}$$	Reviewer-facing assumption.
Compression block	$a=\dfrac{A_sF_y}{0.85f'_m b}$	$$a=\frac{(0.31)(60000)}{(0.85)(2000)(32)}=\frac{18600}{54400}=0.342\ \mathrm{in}$$	Rectangular stress block approximation.
Nominal moment	$M_n=A_sF_y\left(d-\dfrac{a}{2}\right)$	$$M_n=(0.31)(60000)\left(5.75-\frac{0.342}{2}\right)$$ $$=(18600)(5.579)=103{,}769\ \mathrm{lb\!-\!in}$$ $$=\frac{103{,}769}{12}=8.65\ \mathrm{k\!-\!ft}$$	OOP flexure about thickness.
Design moment strength	$\phi M_n$ with $\phi=0.90$	$$\phi M_n=0.90(8.65)=7.78\ \mathrm{k\!-\!ft}$$	Strength reduction for flexure (typ.).
Adequacy	Check: $\phi M_n \ge M_u$	$$7.78\ \mathrm{k\!-\!ft}\ \ge\ 7.72\ \mathrm{k\!-\!ft}\quad\Rightarrow\quad \textbf{OK}$$	Typical partially grouted wall strip is adequate away from openings.

Boundary Condition Note: This check assumes the wall is laterally supported out-of-plane at the top and bottom (roof diaphragm/bond beam and foundation). If a cantilever condition were assumed, the demand would increase substantially.

Conclusion (Typical Wall): For typical wall regions away from openings, MW8 partially grouted construction with vertical #5 @ 32" o.c. provides $\phi M_n \approx 7.78\ \mathrm{k\!-\!ft}$ which meets $M_u \approx 7.72\ \mathrm{k\!-\!ft}$ for $p=33$ psf and $L=26.5$ ft.

2.3 Added Margin Check — Reduce Vertical Reinforcement Spacing to #5 @ 24" o.c.

To provide additional reserve capacity while maintaining an 8" partially grouted wall, a comparative check is performed using reduced vertical reinforcement spacing. All other assumptions remain unchanged.

Step	Expression	Result	Comment
2.3.1	Tributary width: $b_{trib} = 24"/12$	$b_{trib} = 2.00\ \mathrm{ft}$	Reduced tributary width per vertical bar line.
2.3.2	Line load: $w = p\,b_{trib}$	$w = 33(2.00)=66\ \mathrm{plf}$	Lower OOP demand due to reduced spacing.
2.3.3	Moment demand: $M_u=\dfrac{wL^2}{8}$	$$M_u=\frac{(66)(26.5^2)}{8}=\frac{(66)(702.25)}{8}=5.79\ \mathrm{k\!-\!ft}$$	Same simple-span vertical strip assumption (top and bottom support).
2.3.4	Compression block: $a=\dfrac{A_sF_y}{0.85f'_m b}$ with $b=24$ in	$$a=\frac{(0.31)(60000)}{(0.85)(2000)(24)}=\frac{18600}{40800}=0.456\ \mathrm{in}$$	Same single #5 bar area, smaller tributary strip width along wall.
2.3.5	$\phi M_n=0.90\Big[A_sF_y\Big(d-\dfrac{a}{2}\Big)\Big]$	$$\phi M_n=0.90\Big[(0.31)(60000)\Big(5.75-\frac{0.456}{2}\Big)\Big]$$ $$=(0.90)\big[(18600)(5.522)\big]=92{,}433\ \mathrm{lb\!-\!in}$$ $$=\frac{92{,}433}{12}=7.70\ \mathrm{k\!-\!ft}$$	Design flexural strength for a 24" tributary strip with one #5 bar.
2.3.6	Check: $\phi M_n \ge M_u$	$$7.70\ \mathrm{k\!-\!ft}\ \ge\ 5.79\ \mathrm{k\!-\!ft}\quad\Rightarrow\quad \textbf{OK}$$	Provides clear reserve capacity relative to demand.

Conclusion (Added Margin): Reducing vertical reinforcement spacing to #5 @ 24" o.c. increases reserve capacity for typical wall regions under the governing out-of-plane pressure. This adjustment improves robustness while preserving an 8" partially grouted wall construction concept.

3. Note on Openings / Jamb Boundary Elements

This file includes the typical wall check requested (no openings). For large openings (e.g., OH doors), jamb regions are treated as boundary elements and detailed per the Masonry Jamb Schedule (MP-series), with solid grout in reinforced cells per masonry grout notes. Opening jamb calculations may be provided on a companion sheet/page if required.