ACI 318-19: Plain concrete - Nominal shear strength (14.5.5.1)

About this ACI 318-19: Plain Concrete – Nominal Shear Strength (14.5.5.1) Calculator

This calculator checks the nominal shear strength of plain concrete members per ACI 318-19 Section 14.5.5.1, covering both one-way and two-way shear actions using the equations in Table 14.5.5.1. It computes the nominal strength, applies the user-defined strength reduction factor, and checks whether the factored shear demand satisfies the code limit.

• Structural engineer — verify plain concrete slabs, footings, or walls against shear demand without manually resolving which Table 14.5.5.1 equation governs.
• Foundation designer — run one-way and two-way checks on plain concrete spread footings with full traceability of the beta ratio and perimeter terms.
• Checking engineer — audit demand ratios and intermediate values against the ACI 318-19 equations in a single structured page.

The calculator is engineering-grade, fully transparent in its intermediate steps, and ready to save and share within a CalcTree project page.

More Info on ACI 318-19: Plain Concrete – Nominal Shear Strength (14.5.5.1)

Inputs

The calculator requires a small set of clearly defined inputs. The user selects the shear action type — one-way or two-way — which controls which equation from Table 14.5.5.1 is applied. Concrete compressive strength and the lightweight concrete modification factor lambda feed directly into the empirical shear expressions. Member thickness is required for both action types. For one-way shear, the web width is used; for two-way shear, the critical perimeter is used instead. When two-way action is selected, the beta ratio — defined as the ratio of the long side to the short side of the concentrated load or reaction area — is also required, as it governs the (b) equation in Table 14.5.5.1. The factored shear demand and the strength reduction factor for shear are entered separately, keeping the nominal strength calculation independent of the resistance side of the check.

Calculation Method

For one-way shear action, the nominal strength is calculated directly using the single equation from Table 14.5.5.1(a), which scales with web width and member thickness. For two-way shear action, the calculator evaluates both equations from Table 14.5.5.1(b) and (c) independently and takes the lesser of the two as the governing nominal strength. The (b) equation includes a term that reduces capacity when the beta ratio is large, meaning rectangular loaded areas produce lower two-way shear capacity than square ones. The (c) equation provides an upper-bound baseline that is always evaluated alongside it. The common factor built from lambda and the square root of the specified concrete strength appears in all three expressions and is computed once for consistency. The design shear strength is then obtained by multiplying the nominal strength by the user-supplied reduction factor.

Outputs and Design Check

The summary table reports the selected shear action, the computed nominal shear strength, the design shear strength after applying the reduction factor, and the demand ratio. The demand ratio is the factored shear demand divided by the design shear strength — a value at or below one indicates the section is adequate. The shear strength check uses a pass/fail traffic light result tied directly to the demand ratio, giving an immediate read on code compliance. All intermediate quantities are retained in the calculation block so any value can be traced back to its source equation.

Common Calculation Errors to Avoid

• Selecting the wrong shear action type — one-way and two-way shear apply to fundamentally different structural configurations; using the one-way equation for a punching shear situation, or vice versa, produces an incorrect nominal strength and an invalid check.
• Using the net thickness rather than the total member thickness — ACI 318-19 Table 14.5.5.1 uses h, the full plain concrete member thickness, not a reduced effective depth; substituting d leads to unconservative results.
• Ignoring the beta ratio for two-way action — when the loaded area is rectangular, the (b) equation in Table 14.5.5.1 will govern for large beta values; omitting beta and applying only the (c) equation overstates the nominal strength.
• Applying an incorrect lightweight factor — lambda must match the concrete mix; using the normalweight value of 1.0 for lightweight concrete overestimates shear capacity in a non-conservative direction.
• Confusing the critical perimeter with the web width — the two-way perimeter and the one-way web width are distinct geometric quantities; swapping them between action types produces results that are neither physically meaningful nor code-compliant.
• Treating phi as fixed without checking the project basis — ACI 318-19 Section 21.2 assigns phi values based on action type and design approach; confirm that the phi entered matches the applicable condition before running the check.

FAQs

What does ACI 318-19 Section 14.5.5.1 cover for plain concrete shear?

ACI 318-19 Section 14.5.5.1 sets out nominal shear strength for plain concrete members using empirical equations based on concrete compressive strength and member thickness. Unlike reinforced concrete, plain concrete has no shear reinforcement, so the full section thickness h is used directly in the capacity equations rather than an effective depth d. Table 14.5.5.1 provides separate expressions for one-way and two-way shear actions.

What is the difference between one-way and two-way shear action for plain concrete?

One-way shear acts across the full width of a member, like beam shear in a wall or slab strip. Two-way shear is punching action around a concentrated load or column, where failure occurs along a perimeter. ACI 318-19 Table 14.5.5.1 uses b_w and h for one-way, and b_0 and h for two-way. The two-way case also depends on beta, the ratio of the long side to short side of the loaded area, and takes the lesser of two expressions to govern.

When does the two-way beta term actually control the result?

The two-way case uses the lesser of expressions (b) and (c) from Table 14.5.5.1. Expression (b) includes the (1 + 2/beta) factor, which reduces as beta increases. When beta equals 2, expression (b) gives 2 times the base term, which equals expression (c), so both govern equally. For beta greater than 2, expression (c) at 2 times the base term will always be the lesser and will govern. For square loaded areas where beta equals 1, expression (b) gives 3 times the base, so expression (c) still governs.

What value should I use for the lightweight concrete factor lambda?

Use lambda = 1.0 for normal-weight concrete. For lightweight concrete, ACI 318-19 Section 19.2.4 allows lambda = 0.75 for all-lightweight and lambda = 0.85 for sand-lightweight concrete, unless a more precise calculation based on splitting tensile strength is used. Enter the appropriate value directly into the lambda input on this page.

What is phi_v set to and can I change it?

This calculation treats phi_v as a user input rather than hardcoding it. ACI 318-19 Section 21.2.1 specifies phi = 0.60 for plain concrete shear, but project-specific requirements or alternate code editions may use a different value. The default is set to 0.75 in the template, so verify and update this to 0.60 or the value applicable to your project before using results.

How do I interpret the demand ratio output?

The demand ratio is V_u divided by phi_v times V_n. A value below 1.0 means the factored shear demand is within the design shear capacity and the check passes. A value above 1.0 means the section is overstressed and either the geometry, concrete strength, or loading needs to be revised. The traffic light indicator shows pass or fail directly based on this ratio.