Vertical irregularity type 5a and 5b: weak and extreme weak story The shear strengths are given for the piers of the three-story (concrete masonry unit [CMU]) masonry building shown in Figure 3.32, in Table 3.7. Determine if a weak story irregularity exists.

Question

Vertical irregularity type 5a and 5b: weak and extreme weak story
The shear strengths are given for the piers of the three-story (concrete masonry unit [CMU]) masonry building shown in Figure 3.32, in Table 3.7. Determine if a weak story irregularity exists.

Table 3.7 Calculation of diaphragm force at each level
K = 1.10, V = 331 kips
Level	[latex]w_i[/latex] (kips)	[latex]F_i[/latex] (kips)	[latex]F_{px}[/latex] (kips)
6(roofs)	840	100.92	[latex]\frac{100.92}{840}(840)=100.92[/latex]
5	918	88.64	[latex]\left(\frac{88.64+100.92}{840+918}\right)918=98.99[/latex]
4	918	67.46	[latex]\left(\frac{67.46+88.64+100.92}{840+2(918)}\right)918=88.17[/latex]
3	918	46.87	[latex]\left(\frac{46.87+67.46+88.64+100.92}{840+3(918)}\right)918=77.62[/latex]
2	918	27.11
	∑4512	331	[latex]\left(\frac{331}{4512}\right)918=67.34[/latex]

Accepted Answer

The total shear at each floor level is calculated here (Table 3.8):

Table 3.8 Shear strength of piers as labeled in Figure 3.32
Pier #	Shear strength [latex]V_n[/latex](k)
1	15
2	8
3	8
4	15
5	19
6	19
7	19
8	19
9	25
10	25
11	25
12	25

[latex]V_{n_{3rd}}=25+25+25+25=100^k\V_{n_{2nd}}=19+19+19+19=76^k[/latex]

[latex]V_{n_{main}}=15+8+8+15=46^k[/latex]
Check story strength
[latex]V_{n_{2nd}}\lt 0.8 V_{n_{3rd}}[/latex]

[latex]46^k \lt 0.65(76^k)=49.4^k[/latex]
Thus, an extreme weak story irregularity exists.
The following Tables 3.9 and 3.10 summarizes the required analyses and design implications for buildings possessing irregularities and their assigned seismic design categories.

Table 3.9 Horizontal structural irregularities
Type of irregularity	Building’s seismic design category	Summary of analysis and design implications
l(a) Torsion	D, E, F	1) Equivalent lateral force analysis isn’t permitted. (T12.6-1)
1) Applies to rigid and semi rigid diaphragm buildings		2) Seismic design forces are to be increased by 25% for connections of diaphragms to vertical elements and collectors and for collectors and their connections to vertical elements. (12.3.3.4)
	B, C, D, E, F	1) Building must be analyzed using a 3-D model. (12.7.3) 2) Dynamic analysis may be required. (16.2.2)
	C, D, E, F	1) Torsional amplification factor Ax must be used at each level. (12.8.4.3) 2) The design story drift shall not exceed the allowable story drift in T 12.12-1. (12.12.1)
1(b) Extreme Torsion	E, F	Not permitted (12.3.3.1)
1) Applies to rigid and semi rigid diaphragm buildings	D	1) Equivalent lateral force analysis is not permitted. (T12.6-1) 2) Seismic design forces are to be increased by 25% for connection of diaphragms to vertical elements and collectors and for collectors and their connections to vertical elements.
	B, C, D	1) Building must be analyzed using a 3-D model. (12.7.3)
	C, D	1) Torsional amplification factor Ax must be used at each level. (12.8.4.3) 2) The design story drift shall not exceed the allowable story drift in T 12.12-1. (12.12.1)
2. Reentrant corners	D, E, F	1) Seismic design forces are to be increased by 25% for connection of diaphragms to vertical elements and collectors and for collectors and their connections to vertical elements. (12.3.3.4)
3. Diaphragm discontinuity	D, E, F	1) Seismic design forces are to be increased by 25% for connection of diaphragms to vertical elements and collectors and for collectors and their connections to vertical elements. (12.3.3.4)
4. Out-of-plan offsets	B, C, D, E, F	1) Must be designed to resist the seismic load effects including over strength factor of 12.4.3. (12.3.3.3) 2) Building must be analyzed using a 3-D model. (12.7.3) 3) Dynamic analysis may be required. (16.2.2)
	D, E, F	1) Seismic design forces are to be increased by 25% for connection of diaphragms to vertical elements and collectors and for collectors and their connections to vertical elements. (12.3.3.4) 2) Equivalent lateral force analysis isn’t permitted. (T12.6-1)
5. Nonparallel system	C, D, E, F	1) Orthogonal combination procedure is required. Design requires 100% of force for one direction plus 30% of forces in perpendicular direction. (12.5.3)
	B, C, D, E, F	1) Building must be analyzed using a 3-D model. (12.7.3) 2) Dynamic analysis may be required. (16.2.2)
	D, E, F	1) Equivalent lateral force analysis is not permitted. (T12.6-1)

Table 3.10 Vertical structural irregularities
Type of irregularity	Building’s seismic design category	Summary of analysis and design implications
l(a) Soft story 1) Does not apply to one-story buildings 2) Does not apply to two-story buildings in B, C, D seismic categories	D, E, F	1) Equivalent lateral force analysis is not permitted. (T12.6-1)
1(b) Extreme soft story 1) Does not apply to one-story buildings	D, E, F	1) Equivalent lateral force analysis is not permitted. (T12.6-1)
2) Does not apply to two-story buildings in B, C, D seismic categories	E, F	1) Not permitted. (12.3.3.1)
2. Weight(mass) Irregularity 1) Does not apply to one-story buildings 2) Does not apply to two-story buildings in B, C, D seismic categories	D, E, F	1) Equivalent lateral force analysis isn’t permitted. (T12.6-1)
3. Vertical geometric	D, E, F	1) Equivalent lateral force analysis is not permitted. (T12.6-1)
4. In-plane discontinuity	B, C, D, E, F	1) Must be designed to resist the seismic load effects including over strength factor of 12.4.3. (12.3.3.3)
	D, E, F	1) Seismic design forces are to be increased by 25% for connections of diaphragms to vertical elements and collectors and for collectors and their connections to vertical elements. (12.3.3.4) 2) For structures with T > 3.5Ts, equivalent internal force analysis is not permitted. (T12.6-1)
5(a) Weak story	E, F	1) Not permitted. (12.3.3.1)
	D	1) Equivalent lateral force analysis is not permitted. (T12.6-1)
5(b) Extreme weak story	D, E, F	1) Not permitted. (12.3.3.1)
	B, C	1) Maximum permitted height is 30 ft and not over two stories unless designed using the over strength factor. (12.3.3.2)

Typically a building’s irregularities are identified during design and analysis. The designer should carefully consider the implications when designing the lateral force resisting system to minimize as much as possible where appropriate. Often a reasonable modification can effectively eliminate an irregularity

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