Structural Engineering – Reinforced Concrete Design Structures
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CEEN 445 Reinforced Concrete Structures – HWK #9
Assigned: 10/19/2020 Due: 10/30/2020
Note: This homework requires iteration. So it is the perfect time to try doing it in Excel. If you want to do hand
calculation it is OK, but I suggest using Excel table if you want to save time. Please make sure you either copy &
paste your table in your solution, or you will attach an excel file separately for grader to check your calculation.
1. Given the beam dimensions shown. Assume steel in one layer and #3 stirrup, interior exposure,
3
4
” max.
coarse aggregate, 𝑓𝑦 = 60 𝑘𝑠𝑖, for part (1) and (2), use 𝒇𝒄
′ = 𝟓 𝒌𝒔𝒊, for part (4) use 𝒇𝒄
′ = 𝟑. 𝟓 𝒌𝒔𝒊
(1) Find 𝐴𝑠 needed if 𝑀𝑢 = 450 𝑘 ∙ 𝑓𝑡 (need 𝑀𝑛 ≥
𝑀𝑢
𝜙⁄ . Assume initial that 𝜙 = 0.90, determine if
the 𝐴𝑠 you found is ≤ (𝐴𝑠 𝑓𝑜𝑟 𝜀𝑡 = 𝜀𝑡𝑦 + 0.003). if it is not, increase depth of member to 𝑑 =
27
1
2
“, ℎ = 30” and repeat
(2) Find 𝐴𝑠 needed if 𝑀𝑢 = 300 𝑘 ∙ 𝑓𝑡
(3) Select bars for part (1), use bars ≤ #8 and ≤ 2 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡 𝑏𝑎𝑟 𝑠𝑖𝑧𝑒𝑠. Show bars selected can fit in
𝑏 = 18″. If not so, state how many bars of what size are to go into a second layer. If fits the given
beam width, then please show me your detailed layout as we discussed in Example 13-2 as long as
your design satisfy all the ACI 318-14 requirement.
(4) Find 𝐴𝑠 needed if 𝑀𝑢 = 450 𝑘 ∙ 𝑓𝑡. What % of 𝐴𝑠 for 𝜀𝑡 = 𝜀𝑡𝑦 + 0.003 if this value? What % of 𝐴𝑠
found from part (1) is this 𝐴𝑠 value now needed?
2. Given the same beam size, dimensions, and materials as in Problem 1 (𝑓𝑐
′ = 5 𝑘𝑠𝑖). Now, 𝑀𝑢 = 780 𝑘 ∙
𝑓𝑡 and the proposed reinforcement is 2-#9 bars and 8-#8 bars.
(1) Given #9 bars go in the stirrup “corners” of the bottom layer, determine how many of the #8 bars
may go into the bottom layer. If a second layer is needed, place an even number (i.e. 2, 4, 6…) of #8
bars in the second layer. Show on a sketch, the bar arrangement, and better including layout details.
(2) Find d for the bar arrangement you found. What % of 24.5″ is this d?
(3) Find 𝑀𝑛, 𝜀𝑡 and 𝜙𝑀𝑛 assuming 𝑑 = 24
1
2
“, then find 𝑀𝑛 and 𝜙𝑀𝑛 with the d value found in part (2).
Is 𝑀𝑢 ≤ 𝜙𝑀𝑛?