Note:
Recommended Text and/or Course Materials:
- Building Code Requirements and Specification for Masonry Structures (TMS 402-11, ACI 530-11, ASCE 5-11).
- Masonry Designers Guide, 7th Edition (MDG-7); The Masonry Society
Axial Load and Flexure
Problem 1:
A rectangular column is shown below. Determine the P-M interaction curve for SD using the same points we discussed in class for axial load and bending about the weak axis.f’m = 2000 psi and Gr. 60 bars are used. The height of the column is 12 ft.
Problem 2:
Uncle Ed’s Oil shop is where I get my oil change and the front of the store has a configuration like shown on the next page. Big doors are used for cars to come in and get an oil change. Suppose that the masonry column shown in Problem 1 serves as a pilaster as part of the wall. Wind loading in and out of the page is 50 psf on the wall system. Assume the roof line is right at the top of the wall. Load is applied to the roof that transfers to the wall system with 50 psf snow and 35 psf dead. The tributary width of the wall with respect to the loads is 12 ft (similar to example in Lecture 1). Assume the roof load is not eccentric with respect to the wall. Assume normal weight masonry with density = 125 pcf and f’m = 1500 psi. Determine heights by considering all masonry units are nominal 8 in. in depth.
a)Determine the axial loads at midheight of the pilaster for (i) snow and (ii) dead considering all roof dead weight, additional dead weight of the masonry, and roof snow. Must consider tributary width.
b)Determine the unfactored moment due to wind at midheight (assume simply supported)
c)Show that the design is adequate for the following load combinations using the P-M interaction curve developed in Problem 1.
i.1.4D
ii.0.9D + 1.0W
iii.1.2D + 1.6S + 0.5W
iv.1.2D + 1.0W + 0.5 S
Hint: For all cases, I had way more pilaster than I needed. It is overdesigned. But I spent awhile developing and the process can still be understood.
Problem 3:
It is possible to develop a P-M interaction curve for a masonry column using ASD. However, it is very difficult in the cracked condition when you assure masonry stress controls and then you find that steel stress controls. In this problem, I want you to develop a P-M interaction curve for ASD but I’ll guide you through it since it is hard. This is for the column in Problem 1 and again for bending about the weak axis. The P-M interaction curve is a rough approximation.
a)Determine the axial load capacity without moment from pure compression as learned in Lecture 3.
b)Assume that now the beam is subjected to moment as well. What is the maximum moment that can be applied with the axial load in Part a. (Trial and error and computer program required). The section is uncracked.
c)Section is cracked and depth to neutral axis, c, = 9 in. Determine the combined axial load and moment capacity assuming masonry at maximum combined compressive stress.
d)Section is cracked and depth to neutral axis, c, = 6 in. Determine the combined axial load and moment capacity assuming masonry at maximum combined compressive stress.
e)Section is cracked and depth to neutral axis, c, = 3 in. Determine the combined axial load and moment capacity assuming masonry at maximum combined compressive stress.
f)calculate the pure moment condition. It was determined steel stress controlled when P is close to zero. Steel stress should not control for parts c-e but it should be checked for understanding. M = 12.931 k-ft when P = 0 kips.
g)Plot the P-M interaction curve for a-g. Use straight lines for your graph.
Shear Wall Design
Problem 1:
A three-story shear wall is designed assuming wind load controls. The wall is an “ordinary reinforced shear wall” that is grouted. Assume that f’m = 1500 psi and Gr. 60 steel is used. Dead loads are shown on the drawing but add wall self-weight as well. The nominal width of the shear wall is 8 in. The density is 125 pcf. Use combination 0.6D + 0.6W for ASD and 0.9D + W for SD to analyze.
a)For ASD and SD, determine the moment, axial load, and shear at base using combinations.
b)Show that the masonry alone has adequate shear strength per ASD. Consider actual M/Vd.
c)Show that the masonry alone has adequate shear strength per SD. Consider actual Mu/Vudv.
d)Assuming 2 No. 7 at the ends of the wall as shown, prove that the wall has adequate moment capacity per the ASD approach using the assumption it is singly reinforced.
e)Per ASD and ignoring contribution of the steel, show that the axial load capacity is adequate using the bottom story as the unbraced length. Also, check combined stress using a simplified interaction of applied force/stress vs. allowable force/stress ensuring the combined ratio does not exceed 1.0 (see last example Lecture 4).
f)Assuming 2 No. 7 at the ends of the wall as shown, prove that the wall has adequate moment capacity per the SD approach using the assumption it is singly reinforced. Assume axial load and combined strength for axial and flexure okay by inspection.
g)Explain why the vertical reinforcement shown is adequate per detailing rules.
h)Explain why the horizontal reinforcement shown is adequate per detailing rules.
Problem 2:
A three-story shear wall is designed for Seismic Design Category D meaning it is required to be a “special reinforced masonry” shear wall. Assume that f’m = 1500 psi and Gr. 60 steel is used. Fully grouted. Dead loads are shown on the drawing but add wall self-weight as well. The nominal width of the shear wall is 8 in. The density is 125 pcf. (dead weight same as Problem 1) Seismic loads applied to the wall are shown. For academic purposes, ignore the vertical component of earthquake forces and assume that the loads shown are the E in earthquake load combinations (from lecture notes, ignore Ev and only consider Eh). Only design the problem per the SD approach for steps e-g. Show that the reinforcement details are adequate by performing the following steps:
a)Show that the horizontal reinforcement is in acceptable limits for gross area and passes the maximum spacing checks.
b)Show that the vertical reinforcement is in acceptable limits for gross area and passes the maximum spacing checks.
c)Show that the combined horizontal and vertical reinforc. ratio is within an acceptable limit.
d)Indicate why the bars are properly placed near edges of the wall.
e)Prove that the masonry itself has adequate shear capacity. Use combination 0.9D+E.
f)Due to the generation of a plastic hinge, show that the horizontal steel reinforcement alone has adequate capacity for the applied shear force. Use 0.9D + E.
g)Use an approach similar to that of Page 15 of the lecture notes to prove that the combination of axial load and moment is acceptable. Use 0.9D+E. Hint: Figure out the strain condition such that the design axial load is equal to the applied axial load and check moment.