Shear Wall Sample Problem

Transcription

1 Shear Wall Sample Problem A long by high concrete block masonry shear wall, reinforced with 4 No. 20 bars (, as shown in the figure below, is subjected to a factored axial load of (including the self-weight) and a factored shear load of. Using concrete blocks, with a specified compressive strength of, Type-S mortar, and only grouting those cells with reinforcement, determine whether the wall can resist the applied loads. a) Calculate the in-plane bending resistance. b) Calculate the in-plane shear resistance, including sliding shear. P f = 80 kn V f = 85 kn 4.6 m 2.6 m All dimensions are in mm and are to centreline of reinforcement. 1 P a g e

2 At modular length, the long wall is composed of A well recognized method to simplify calculations, is possible to smear the grout along the length of the wall (Masonry Structures, Section 9.6.1). That is, average out the grouted cells over the length of the web, to determine an effective wall thickness. This method simplifies the wal dimensions so they are constant along the length of the partially grouted wall. An effective compressive strength is also determined to account for smearing effects: Determine the neutral axis, assuming that it lies between bar 3 & 4 (and that bars 1 & 2 yields and 3 doesn t): Assuming the two bars on the far left are yielding: 2 P a g e

3 Determining the tension in the third bar, assuming it does not yield: As can be seen, the neutral axis does in fact lie within the third and fourth bar. Check to make sure the first and second bar yields: Determine the tension in reinforcement: 3 P a g e

4 Determine the compression in masonry: Determine moment capacity (moment resistance), about the centroid of the wall: Hand Calculation MASS * * ** ** *Note: There is a difference in the moment capacity determined by hand, and that determined by MASS TM. There are two reasons for this. When smearing effects are applied by MASS TM, the program divides the wall into segments. The endzones are calculated seperatly from the smeared region within the web. This may result in a slightly unconservative design. In addition is used to determine when should be used. This may result in a slightly more conservative design. **The sample problem stated that the axial load and point load were already factored. Loads entered into the program should be unfactored. The program automatically determines the appropriate load combinations based on the applied loads and importance category selected. Because the program adds on the effect of different 4 P a g e

5 factors, the loads are entered as dead loads and divide by 1.4 to remove the factor. That is, the axial load entered using MASS s Loads tab is entered as Likewise, the shear load is entered as. Determine the in-plane shear: The masonry does not have enough shear capacity, therefore horizontal steel is needed. Determine the minimum area of steel required: 5 P a g e

6 Choosing a spacing of for example, the following minimum steel area is required: This can be readily satisfied with a number of steel configurations. For instance, by placing No. 10 bond beams at. The total shear resistance is then: Hand Calculation MASS *** *** 0 *** ***This is a known bug found within MASS Version 1.0 and is described on the MASS TM website MASS TM Version 1.0 cycles through all of the load combinations to determine the maximum factored shear and corresponding location along the wall height. This routine starts at the top of the wall and checks all points down the height of the wall. If the factored shear along the height of the wall is constant, the location of maximum shear will be the first point checked. In MASS TM Version 1.0, this first point is at the top of the wall. For a cantilevered shear wall, the factored shear profile is going to be constant along the height and therefore the location of maximum shear picked by MASS TM Version 1.0 will always be at the top of the wall. If there is no applied moment at the top of the wall, as in this example, the factored moment 6 P a g e

7 at the location of maximum factored shear will be zero and therefore, is assigned the minimum code value of However, in some cases, depending on the ratio of and, the critical location for shear design might be at the bottom of the wall as shown in this example since may range upto the maximum value of 1.0. As a result, the masonry shear strength calculated in MASS may be over estimated. 7 P a g e