Прочность на сдвиг по ACI 318-19 в RFEM 6

Введение

В предыдущей норме ACI 318-14 [2] были указаны восемь уравнений для расчета прочности на сдвиг V_c - без учета пределов применения. Пользователь, кроме того, может выбрать между упрощенным и точным методом расчета. Целью нового концепта в ACI 318-19 было, кроме прочего, уменьшение количества расчетных уравнений для V_c. Концепт должен был также учесть влияние высоты элемента, коэффициента продольного армирования и осевого напряжения.

Прочность на сдвиг V_c по норме ACI 318-19

For non-prestressed reinforced concrete beams, the shear resistance V_c is calculated according to ACI 318-19 [1] with Equations a) to c) from Table 22.5.5.1. With the new Equations b) and c), the member height, the longitudinal reinforcement ratio, and the normal stress now influence the shear strength, V_c. Equation a) was basically taken from ACI 318-14 [2].

The determination of the shear resistance V_c according to Table 22.5.5.1 [1], depends on the inserted shear reinforcement A_v. При наличии или превышении объема минимального работающего на сдвиг армирования A_v,min по п. 9.6.3.4 расчет V_c может быть выполнен по уравнению а)

или по уравнению b)

from Table 22.5.5.1 [1].
If you compare the two equations shown above, you can see that in Equation b), the factor 2 λ has been replaced by the term 8 λ (ρ_w)1/3. Коэффициент продольной арматуры ρ_w таким образом влияет на расчет прочности на сдвиг V_c. Image 01 shows the distribution of 8 λ (ρ_w)1/3 as a function of ρ_w (with λ = 1).

При λ = 1,0 выражение 8 λ (ρ_w)^1/3 равно значению 2 λ при коэффициенте продольной арматуры ρ_w = 1,56 %. When calculating V_c, Equation a) for λ= 1 and a longitudinal reinforcement ratio ρ_w (greater than) 1.56% and Equation b) for λ= 1 and ρ_w > 1.56% results in the greater concrete shear resistance. The standard allows the application of both equations. Therefore, the maximum value from Equations a) and b) can be used for a cost-effective design.

For beams with shear reinforcement A_v less than A_v,min, Equation c) of Table 22.5.5.1 [1] is to be used according to ACI 318-19 [1].

За исключением переменной λ_s уравнение c) аналогично уравнению b), рассмотренному выше. For structural components with little or no shear reinforcement, the concrete shear resistance V_c decreases with increasing structural component height. При вводе коэффициента λ_s учитывается так называемый «Size Effect». The factor λ_s is determined according to Equation 22.5.5.1.3 [1] as follows.

The reduction of the shear resistance V_c,c by the factor λ_s is only effective for structural heights d (greater than) 10in. На рисунке 02 показана диаграмма выражения 8 λ_s λ (ρ_w)^1/3 при различных значениях статической полезной высоты d.

Пример: Рассчитать требуемую работающую на сдвиг арматуру по ACI 318-19

The following section describes how to determine the required shear reinforcement according to the new concept of ACI 318-19 [1] for a reinforced concrete beam, which was designed in a previous Knowledge Base Article according to ACI 318-14 [2]. На рисунке 03 показаны конструктивная модель и расчетные нагрузки.

The rectangular cross-section has the dimensions 25 in. · 11 in. The concrete has a compressive strength of f'_c = 5,000 psi. The yield strength of the reinforcing steel used is f_y = 60,000 psi. The effective depth of the tension reinforcement is applied with d = 22.5 in. The design value of the acting shear force V_u at a distance d from the support is 61.10 kips.

The determination of the shear resistance V_s according to Table 22.5.5.1 [1] depends on the height of the inserted shear reinforcement A_v. The prerequisite for using Equations a) and b) is that the minimum shear reinforcement according to 9.6.3.4 [1] is applied. For this reason, a check is performed in the first step as to whether a minimum reinforcement has to be considered according to 9.6.3.1 [1].

61,10 тыс. фунтов > 13,13 тыс. фунтов

Требуется минимальное поперечное армирование. This is calculated according to 9.6.3.4 [1], as follows.

a_v,min = 0,12 кв. дюймов/фут

When considering the minimum shear reinforcement, the concrete shear resistance V_c can now be determined with Equations a) or b) of Table 22.5.5.1 [1]. The shear resistance V_c,a according to Equation a) is calculated as V_c,a = 35.0 kips. To apply Equation b), it is necessary to know the longitudinal reinforcement ratio ρ_w. To be able to compare the calculated shear reinforcement with the calculation result of the Concrete Design Add-on, ρ_w is determined with the required longitudinal reinforcement at the distance d from the support. A bending moment of M_y,u = 1533 kip-in results in a longitudinal reinforcement of A_s,req = 1.33 in², which is ρ_w = 0.536%. Image 01 shows the influence of the longitudinal reinforcement ratio ρw on the calculation of V_c,b. Since ρ_w (less than) 1.5% here, Equation b) will result in a lower shear resistance V_c,b than Equation a) and we can skip determining V_c,b. However, we calculate V_c,b to show it.

V_c,b = 24,52 тыс. фунтов

Как и ожидалось, по уравнению b) получена более низкая прочность на сдвиг, чем по уравнению а).

Additionally, the shear resistance V_c is limited to the maximum value V_c,max according to 22.5.5.1.1 [1].
a_v,min = 0.12 in²/ft

When considering the minimum shear reinforcement, the concrete shear resistance V_c can now be determined with Equations a) or b) of Table 22.5.5.1 [1].

Прочность на сдвиг V_c,a по уравнению a) равна V_c,a = 35,0 тыс. фунтов.

Для применения уравнения b) необходимо знать значение коэффициента продольного армирования ρ_w. To be able to compare the calculated shear reinforcement with the calculation result of the Concrete Design Add-on, ρ_w is determined with the required longitudinal reinforcement at the distance d from the support. A bending moment of M_y,u = 1533 kip-in results in a longitudinal reinforcement of A_s,req = 1.33 in², which is ρ_w = 0.536%. Image 01 shows the influence of the longitudinal reinforcement ratio ρ_w on the calculation of V_c,b. Since ρ_w (greater than) 1.5% here, Equation b) will result in a lower shear resistance V_c,b than Equation a) and we can skip determining V_c,b. However, we calculate V_c,b to show it.

V_c,b = 24,52 тыс. фунтов

Как и ожидалось, по уравнению b) получена более низкая прочность на сдвиг, чем по уравнению а).

Additionally, the shear resistance V_c is limited to the maximum value V_c,max according to 22.5.5.1.1 [1].

V_c,max = 87,5 тыс. фунтов

Наконец, для расчета требуемой работающей на сдвиг арматуры получена следующая применяемая прочность бетона на сдвиг V_c.

V_c = max [V_c,a ; V_c,b ] ≤ V_c,max

V_c = [35,0 тыс. фунтов; 24,5 тыс. фунтов] ≤ 87,5 тыс. фунтов

V_c = 35,0 тыс. фунтов

The required shear reinforcement req. a_v is calculated as follows:

Req. a_v = 0.41 in²/ft ≥ 0.12 in²/ft

The reinforced concrete design according to ACI 318-19 [1] can be performed with RFEM 6. The Concrete Design Add-on also calculates a required shear reinforcement of 0.43 in²/ft at the distance d from the support (see Image 04).

Внимание! The results in RFEM 6 differ from the hand calculations slightly due to a more accurate value for the Depth (d) calculated. RFEM 6 takes into account that there are multiple layers of tension reinforcement where the hand calculations assume a single layer.

Наконец, выполняется проверка максимальной несущей способности сжатого раскоса фермочной конструкции по п. 22.5.1.2.

61.10 kips ≤ 175.00 kips.

Расчет на сдвиг по норме ACI 318-19 выполнен.
Как и ожидалось, по уравнению b) получена более низкая прочность на сдвиг, чем по уравнению а).

Additionally, the shear resistance V_c is limited to the maximum value V_c,max according to 22.5.5.1.1 [1].

Заключение

ACI 318-19 [1] introduced a new concept to determine the shear resistance V_c. При этом удалось сократить до трех количество возможных расчетных уравнений из предыдущей версии и включить в расчет влияние нормальных напряжений, высоты элемента и коэффициента продольного армирования. Это упростило расчет прочности на сдвиг V_c.