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ANALYSIS OF TWO-WAY SLABS WITH BEAMS 1

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In this lecture the moments are determined by the direct design method for an exterior panel of a two-way slab with beams. It is felt that if you can handle this problem, you can handle any other case that may arise in flat plates, flat slabs, or two-way slabs with beams using the direct design method. The requirements of the Code are so lengthy and complex that in Example 16.4, which follows, the steps and appropriate Code sections are spelled out in detail. The practicing designer should obtain a copy of the CRSI Design Handbook, because the tables therein will be of tremendous help in slab design. 2

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Example 16.4 SOLUTION ANALYSIS OF TWO-WAY SLABS WITH BEAMS 3

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ANALYSIS OF TWO-WAY SLABS WITH BEAMS 11

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ANALYSIS OF TWO-WAY SLABS WITH BEAMS 12

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ANALYSIS OF TWO-WAY SLABS WITH BEAMS 13

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ANALYSIS OF TWO-WAY SLABS WITH BEAMS 14

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ANALYSIS OF TWO-WAY SLABS WITH BEAMS 15

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ANALYSIS OF TWO-WAY SLABS WITH BEAMS 16

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TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS 17

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TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS On many occasions the maximum load that a two-way slab can support is dependent upon the strength of the joint between the column and the slab. Not only is the load transferred by shear from the slab to the column along an area around the column, but also there may be moments that have to be transferred as well. The moment situation is usually most critical at the exterior columns. If there are moments to be transferred, they will cause shear stresses of their own in the slabs, as will be described in this section. Furthermore, shear forces resulting from moment transfer must be considered in the design of the lateral column reinforcement (that is, ties and spirals), as stated in Section 11.11.1 of the Code. When columns are supporting slabs without beams (that is, flat plates or flat slabs), the load transfer situation between the slabs and columns is extremely critical. Perhaps if we don’t have the flexural reinforcing designed just right throughout the slab as to quantities and positions, we can get by with it; however, if we handle the shear strength situation incorrectly, the results may very well be disastrous. 18

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TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS The serious nature of this problem is shown in Figure 16.20, where it can be seen that if there is no spandrel beam, all of the total exterior slab moment has to be transferred to the column. The transfer is made by both flexure and eccentric shear, the latter being located at a distance of about d/2 from the column face. Section 13.6.3.6 of the Code states that for moment transfer between the slab and edge column, the gravity load moment to be transferred shall be 0.3M o (where M o is the factored statical moment). When gravity loads, wind or earthquake loads, or other lateral forces cause a transfer of an unbalanced moment between a slab and a column, a part of the moment equal to γ f M u shall be transferred by flexure, according to ACI Section 13.5.3.2. Based on both tests and experience, this transfer is to be considered to be made within an effective slab width between lines that are located 1.5 times the slab or drop panel thickness outside opposite faces of the column or capital. The value γ f is to be taken as 19

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TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS 20

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TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS 21

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TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS 22

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TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS 23

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Example 16.5 TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS 24

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Example 16.5 SOLUTION TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS 25

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Example 16.5 SOLUTION TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS 26

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Example 16.5 SOLUTION TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS 27

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Example 16.5 SOLUTION TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS 28

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Example 16.5 SOLUTION TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS 29

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Example 16.5 SOLUTION TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS 30

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TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS If there is an unbalanced loading of two adjoining spans, the result will be an additional moment at the connection of walls and columns to slabs. The Code (13.6.9.2) provides the approximate equation listed at the end of this paragraph to consider the effects of such situations. This particular equation was derived for two adjoining spans, one longer than the other. It was assumed that the longer span was loaded with dead load plus one- half live load and that only dead load was applied to the shorter span. Factored Moments in Columns and Walls 31

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TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS If there is an unbalanced loading of two adjoining spans, the result will be an additional moment at the connection of walls and columns to slabs. The Code (13.6.9.2) provides the approximate equation listed at the end of this paragraph to consider the effects of such situations. This particular equation was derived for two adjoining spans, one longer than the other. It was assumed that the longer span was loaded with dead load plus one- half live load and that only dead load was applied to the shorter span. Factored Moments in Columns and Walls 32

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