How is the skewback angle and keystone taper angle calculated?

In accordance with BIA Technical Notes 31A, the skewback angle is determined by the horizontal slope (overhang) relative to the vertical arch depth: theta = arctan(skewback slope / arch depth). For a standard 12-inch arch depth with a 4-inch skewback overhang, the skewback inclination is arctan(4 / 12) = 18.4 degrees (with keystone half-taper angles of ~9.5 degrees per side). All radiating mortar joints between brick wedges must align with the origin intersection point of the two inclined skewback planes.

Why is upward camber required for flat brick jack arches, and how much camber should be built into the formwork?

Flat masonry soffits are susceptible to optical illusion sagging—appearing to droop at mid-span even when perfectly level—and slight elastic joint compression once temporary wood centering is removed. BIA Technical Notes 31A recommends constructing temporary timber centering with an intentional upward camber crown of 1/8 inch per foot of clear opening span (e.g., 3/8 inch for a 36-inch span or 1/2 inch for a 48-inch span). This camber offsets initial mortar joint settlement and ensures the finished intrados reads dead level to the human eye.

How much horizontal thrust is generated by a flat jack arch, and what masonry abutment width is required?

Because a jack arch has minimal rise, horizontal skewback thrust is significantly higher than in segmental or semicircular arches. Under standard masonry design approximations (Thrust ≈ W * Span / (2 * Depth)), an opening carrying 800 plf uniform tributary load with a 36-inch span and 12-inch depth exerts roughly 2,400 lbs of outward lateral thrust against each skewback. Under light veneer loads, thrust ranges from 300 to 800 lbs. To resist this thrust without diagonal cracking or outward spread, flanking masonry abutment piers must measure at least 24 to 36 inches of solid masonry or incorporate concealed steel tension ties.

When can temporary centering support and shoring be safely struck (removed)?

Temporary wood centering must remain fully wedged and undisturbed until the mortar has cured to at least 70% of its 28-day design compressive strength. Under standard curing conditions (above 50°F / 10°C), temporary centering should remain in place for a minimum of 7 full days for Type S mortar and 10 to 14 days for Type N mortar. Centering should be lowered gradually using hardwood easing wedges or screw jacks to transfer compressive load smoothly into the masonry voussoirs rather than knocking supports out abruptly.

BIA Technical Notes 31A Masonry Design

Jack Arch Calculator

Direct Answer: A 36-inch span flat brick jack arch with a 12-inch depth and 4-inch skewback requires 12 tapered brick wedges set at a 9.46-degree keystone taper angle, creating 300 lbs of outward thrust supported on temporary shoring.

Calculate keystone taper angles, voussoir wedge counts, outward horizontal skewback thrust, required upward camber, and temporary centering shoring for structural flat brick masonry jack arches.

BIA Technical Notes 31A Jack Arch PresetsFlat Brick Lintel Geometry

Wedge Bricks & Taper18.4° Taper

16 Wedges• 2,400 lbs thrust

Details

Clear Opening Span (Inches)= 3.00 ft clear width

Clear horizontal rough opening distance between opposing masonry jambs (typically 24" to 48" for unreinforced jack arches).

Arch Depth / Height (Inches)

Vertical height of the brick lintel courses from soffit intrados to top extrados.

Skewback Slope / Overhang (Inches)

Horizontal setback angle cut at each jamb (BIA 31A recommends 1" slope per 3" depth = 4" on 12" arch).

BIA Technical Notes 31A Design Criteria

The Skewback Principle: Jack arches have horizontal top and bottom chords, but operate in pure compression through radiating voussoirs. The inclined skewback face acts as an abutment skew that transmits gravity dead and live loads into horizontal thrust:Thrust ≈ (800 plf × Span) / Depth.

Upward Camber Requirement: Build temporary wooden centering with a minimum crown camber of 1/8" per foot of span. This counteracts optical sag and slight plastic deformation before the mortar reaches full compressive design strength.

Jack Arch Takeoff

Keystone Taper & VoussoirsBIA 31A

Keystone Taper

18.4°

~9.2° taper / side

Brick Wedges

Tapered voussoir units

Outward Thrust

2,400 lbs

Lateral thrust at skewbacks

Shoring Form

3 sq ft

Centering soffit deck

Center Camber Crown~3/8" (0.38")

Provide 1/8" upward crown per foot of span in timber centering to eliminate optical sag and initial mortar joint deflection.

Jamb Abutment Pier Requirement

Provide at least 24" of solid masonry jamb width on either side of the rough opening to resist the 2,400 lbs lateral outward thrust without spread.

Confirm product yields, unit core volumes, supplier pack sizes and local prices before ordering. Reinforcement quantities are material allowances; laps, hooks, embedment and engineered design are excluded.

Standard Brick Jack Arch Geometry & Skewback Schedules

In accordance with Brick Industry Association (BIA) Technical Notes 31A, flat jack arches convert vertical dead and live loads into horizontal compression thrust. The table below details recommended skewbacks, taper angles, voussoir counts, and centering camber across common opening widths.

32 in (2.67 ft)12 in (4 courses)

Skewback4 in overhang

Keystone Taper18.4° (9.2°/side)

Wedges Required15 voussoirs

Skewback Thrust~2,133 lbs

Formwork Camber5/16 in crown

36 in (3.00 ft)12 in (4 courses)

Skewback4 in overhang

Keystone Taper18.4° (9.2°/side)

Wedges Required16 voussoirs

Skewback Thrust~2,400 lbs

Formwork Camber3/8 in crown

42 in (3.50 ft)12 in (4 courses)

Skewback4 in overhang

Keystone Taper18.4° (9.2°/side)

Wedges Required19 voussoirs

Skewback Thrust~2,800 lbs

Formwork Camber7/16 in crown

48 in (4.00 ft)16 in (5-6 courses)

Skewback4 in overhang

Keystone Taper14.0° (7.0°/side)

Wedges Required21 voussoirs

Skewback Thrust~2,400 lbs

Formwork Camber1/2 in crown

60 in (5.00 ft)16 in (5-6 courses)

Skewback5 in overhang

Keystone Taper17.4° (8.7°/side)

Wedges Required26 voussoirs

Skewback Thrust~3,000 lbs

Formwork Camber5/8 in crown

Clear Span	Arch Depth	Skewback Overhang	Keystone Taper Angle	Wedge Bricks	Skewback Thrust	Centering Camber
32 in (2'-8")	12 in (nominal 4 courses)	4.0 in (1:3 slope)	18.4° (~9.2°/side)	15 tapered voussoirs	2,133 lbs	5/16 in upward crown
36 in (3'-0")	12 in (nominal 4 courses)	4.0 in (1:3 slope)	18.4° (~9.2°/side)	16 tapered voussoirs	2,400 lbs	3/8 in upward crown
42 in (3'-6")	12 in (nominal 4 courses)	4.0 in (1:3 slope)	18.4° (~9.2°/side)	19 tapered voussoirs	2,800 lbs	7/16 in upward crown
48 in (4'-0")	16 in (nominal 5-6 courses)	4.0 in (1:4 slope)	14.0° (~7.0°/side)	21 tapered voussoirs	2,400 lbs	1/2 in upward crown
60 in (5'-0")	16 in (nominal 5-6 courses)	5.0 in (1:3.2 slope)	17.4° (~8.7°/side)	26 tapered voussoirs	3,000 lbs	5/8 in upward crown

Note: Thrust approximations assume an illustrative 800 plf uniform tributary masonry dead and live load. Actual thrust varies with wall height above opening, floor/roof bearing loads, and arch rise-to-span geometry under TMS 402/602 and BIA Technical Notes 31A.

1. Structural Mechanics of Flat Jack Arches (BIA Notes 31A)

A brick jack arch (also termed a flat arch) is an ingenious classical masonry structure designed to span wall openings with a completely horizontal bottom soffit (intrados) and flat top surface (extrados). Unlike reinforced concrete lintels or steel angle irons, which carry vertical gravity loads through tensile flexural bending, an unreinforced masonry jack arch resists loads strictly through pure compressive arch action.

The structural system relies on radiating wedge-shaped brick units (termed voussoirs) oriented on angled mortar bed joints that project downward to a common imaginary focal point below the center of the opening. When vertical gravity loads bear on the top of the arch, the tapered geometry wedges the bricks tightly together, driving internal compressive stresses outward into the inclined skewbacks at the jambs.

Keystone (Central Wedge)

The central symmetrical voussoir that locks the arch assembly under compression. Its double-angled sides set the radiating geometry for all adjacent voussoirs down to the skewback.

Voussoirs (Tapered Wedges)

The tapered brick units that flank the keystone on both sides. In gauge work, bricks are individually cut or ground to a taper; in standard field work, wedge-shaped mortar joints accommodate the angle.

Skewback (Inclined Abutment)

The inclined bearing surface cut into the flanking jamb masonry at the springing line. The skewback angle establishes the thrust line and redirects vertical gravity load into outward lateral thrust.

2. Skewback Cutting Geometry & Keystone Taper Angle

The skewback is the angled masonry surface at each jamb upon which the arch rests. In BIA Technical Notes 31A, the skewback angle is defined by the horizontal setback distance (slope) relative to the vertical depth of the arch. Proper skewback geometry is vital: if the skewback is cut too steep (near vertical), the voussoirs may slip downward under load; if cut too shallow, excessive outward horizontal thrust can rupture the flanking jamb piers.

BIA 31A Skewback Angle & Taper Mathematical Formulas:

Skewback Inclination Angle (θ)

θ = arctan(Skewback Slope / Arch Depth)

Angle of skewback face relative to vertical jamb face.

Brick Wedge Unit Takeoff (N)

N = ceil((Span + 2 × Slope) / 2.75")

Total voussoirs required along extrados chord at 2-3/4" module.

Standard Recommendation: For typical 12-inch arch depths (nominal 4-5 brick courses), BIA 31A recommends a skewback slope of 1 inch per 3 inches of arch depth (4 inches total overhang). This yields an optimal skewback inclination angle of arctan(4 / 12) = 18.4°, balancing mechanical wedge locking with manageable lateral thrust.

3. Upward Camber & Temporary Timber Centering Shoring

A flat jack arch must never be laid out on a perfectly horizontal formwork surface. Two critical mechanical and perceptual realities demand an intentional upward crown (camber):

Elimination of the "Optical Sag" Illusion:Human visual perspective causes a mathematically horizontal masonry opening to appear to sag or droop in the center when framed by tall vertical jambs. An intentional upward crown ensures the finished soffit reads dead-level to the eye.

Accommodation of Initial Elastic Joint Deflection:When temporary wood shoring is loosened, the arch settles slightly as vertical loads transfer into the mortar joints. Camber prevents the bottom intrados from settling below horizontal alignment.

Camber Rule of Thumb: 1/8 Inch Per Foot of Clear Opening Span

BIA Technical Notes 31A mandates an upward camber of 1/8 inch (0.125") for every 1 foot of clear span. For a 36-inch (3-foot) window opening, the timber falsework centering must be cut with a smooth parabolic or curved crown peaking at 3/8 inch (0.375") above the springing line at midspan. For a 48-inch door opening, the center crown is 1/2 inch (0.50").

Centering Removal Timeline (Striking Falsework)

Never knock out or shock timber centering props. Centering must be supported on paired hardwood easing wedges or screw jacks and left in place until the mortar attains at least 70% of design compressive strength:

ASTM C270 Type S Mortar: Maintain shoring minimum 7 full days under normal temperatures (>50°F / 10°C).
ASTM C270 Type N Mortar: Maintain shoring minimum 10 to 14 full days before easing wedges.
Striking Procedure: Gently drive back easing wedges symmetrically from center outward to let voussoirs engage in gradual compression without impact cracking.

4. Outward Horizontal Skewback Thrust & Jamb Abutment Width

Because a jack arch has essentially zero vertical rise compared to a segmental or semicircular arch, the outward horizontal thrust developed at the skewbacks is substantially higher. Gravity forces bearing downward on the flat voussoirs are redirected almost entirely horizontally into the flanking jambs.

Approximate Horizontal Skewback Thrust FormulaBIA 31A Design Aid

Thrust (lbs) ≈ (W × Span) / Depth

Where W = total uniform tributary load (plf), Span = clear opening width (ft), and Depth = arch height (ft).

For a 36-inch (3-foot) span carrying an illustrative 800 plf uniform tributary load with a 12-inch (1-foot) arch depth, the outward skewback thrust is approximately (800 × 3) / 1 = 2,400 lbs. If the opening carries only light veneer self-weight, thrust typically ranges from 300 to 800 lbs.

Minimum Flanking Pier Width Requirement:

To prevent the outward thrust from spreading the jambs or causing diagonal stair-step shear cracking, flanking masonry piers should measure at least 24 to 36 inches of solid masonry on each side of the opening, or be backed by continuous reinforced bond beam CMU with structural tie rods.

5. Worked Engineering Example: 36-Inch Standard Entry Jack Arch

Walk through a complete takeoff calculation for a standard residential exterior entrance rough opening under BIA Technical Notes 31A standards.

Clear Opening36.0 inches (3.0 ft)

Arch Depth12.0 inches (1.0 ft)

Skewback Slope4.0 inches (1:3 ratio)

Step 1: Calculate Skewback Inclination & Keystone Taper Angle

θ = arctan(Slope / Depth) = arctan(4 / 12) = arctan(0.3333) = 18.43°

The skewback cut angles back 18.4° from vertical (71.6° from horizontal bed). The central keystone tapers at approximately 9.2° per side to match the radiating focus.

Step 2: Determine Required Brick Wedges (Voussoirs)

Total Top Extrados Width = Span + (2 × Slope) = 36" + (2 × 4") = 44.0 inches

Wedges Count = ceil(44.0 / 2.75") = ceil(16.0) = 16 tapered brick voussoirs

The assembly requires 1 central symmetrical keystone and 15 flanking tapered voussoir units (7 on one side, 8 on the other, or 17 units total for symmetrical odd-count layout).

Step 3: Calculate Temporary Centering Deck Area

Centering Area = (Span in Feet) × (Depth in Feet) = (36 / 12) × (12 / 12) = 3.0 × 1.0 = 3.0 sq ft

Construct temporary timber soffit formwork deck covering at least 3.0 sq ft of soffit and face shoring.

Step 4: Compute Upward Camber Recommendation

Camber Crown = Span (ft) × (1/8 inch / ft) = 3.0 × 0.125" = 0.375" (3/8 inch)

Form the timber centering with a smooth 3/8-inch upward crown at center to counteract post-striking deflection and visual sag.

Step 5: Compute Outward Skewback Thrust Demand

Horizontal Thrust = (800 plf × 3 ft) / 1 ft = 2,400 lbs lateral thrust at each skewback

Ensure adjacent solid masonry jambs provide at least 24 inches of continuous pier width to safely anchor the 2,400 lbs thrust.

Calculation Assumptions & References Planning Reference

Material estimates depend on the selected dimensions, product yields, and waste allowance.

Content date: October 2026

Related references: BIA Technical Notes 31A (Brick Masonry Arches: Jack, Segmental & Semicircular), TMS 402/602 (Building Code Requirements and Specification for Masonry Structures), ASTM C216 (Standard Specification for Facing Brick), ASTM C902 (Standard Specification for Pedestrian and Light Traffic Paving Brick), ASTM C270 (Standard Specification for Mortar for Unit Masonry). Confirm the applicable edition and local requirements.

A material estimate is not a structural design or code approval.

Masonry Q&A

Brick Jack Arch & Flat Lintel FAQ

Authoritative structural engineering answers on flat brick arch geometry, skewback taper cuts, outward thrust, and centering camber.

A brick jack arch (also called a flat arch) is a structural compression system where individual tapered brick voussoirs and a central keystone radiate from a common focal origin below the opening. Although its bottom intrados soffit and top extrados are horizontal, gravity loads are redirected into pure compressive arch thrust toward the inclined skewbacks at each jamb. This arch action eliminates tensile bending stresses, allowing unreinforced brick masonry to span rough openings without an exposed steel angle lintel, provided flanking jamb piers have adequate mass to resist outward horizontal thrust.