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Prestressed Concrete: A Fundamental Approach

Edward Nawy

Chapter 13

SEISMIC DESIGN OF PRESTRESSED CONCRETE STRUCTURES - all with Video Answers

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Chapter Questions

Problem 1

A $3 \times 18$ panel ductile, moment-resistant frame category-II site-class $B$ frame building has a ground story $15 \mathrm{ft}$. high $(4.6 \mathrm{~m})$ and ten upper stories of equal height of $11^{\prime}-6$ " $(3.5 \mathrm{~m})$. Compute the seismic base shear $V$ and the overturning moment at each story level in terms of the weight $W_s$ of each floor. Use the equivalent lateral force method in the solution. Given:
$$
\begin{aligned}
& S_1=0.34 \mathrm{sec}, S_s=0.90 \sec R=5, \\
& W_s \text { per floor }=2400 \mathrm{kips}(9560 \mathrm{kN})
\end{aligned}
$$

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Problem 2

A moment-resisting ductile frame building is located in a high-seismic-intensity zone. The earthquake forces are resisted equally as a dual system by the ductile frame and a monolithic reinforced concrete shear wall over the total height of the building. The geometry of the structure is given below. Design the shear wall assuming that the magnitude of the loads, forces and moments applied to the wall are 110 percent of the values used in Ex. 13.2. Given:
floors have slabs of thickness $h_f=7$ in. $(178 \mathrm{~mm})$
clear beam spans in both longitudinal and transverse directions $=20^{\prime}-0^{\prime \prime}(6.1 \mathrm{~m})$
shear wall base length $l_w=25 \mathrm{ft}(39.6 \mathrm{~m})$
$$
\begin{aligned}
& \text { shear wall height } h_w=130 \mathrm{ft}(39.6 \mathrm{~m}) \\
& f_c^{\prime}=5000 \mathrm{psi}, \text { normal weight }(34.5 \mathrm{MPa}) \\
& f_{y v}=f_{y h}=60,000 \mathrm{psi}(414 \mathrm{MPa})_v
\end{aligned}
$$

Sketch the wall reinforcement.

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Problem 3

A precast shear wall in a moderate seismicity zone for a six story frame building has a wall thickness of $10 \mathrm{in}$. $(254 \mathrm{~mm})$. The height of each story is $11^{\prime}-6^{\prime \prime}(3.5 \mathrm{~m})$ and the wall segments extend the height of the building and prestressed vertically. The wall is subjected to a factored seismic base shear $V_u=210 \mathrm{kips}(1048 \mathrm{kN})$ and a factored overturning moment $M_e=8000 \mathrm{ft}$-kip $(12,150 \mathrm{kN}-\mathrm{m})$ for Case II loading as controlling in this case (gravity load dominant). The total weight of each floor including any attached masses is $2800 \mathrm{kips}(12,454 \mathrm{kN})$. Design the connection at the base of the wall assuming that the neutral axis obtained by strain-compatibility analysis is $c=21.5$ in. (546 $\mathrm{mm})$. Given:
$$
\begin{aligned}
& \text { sliding coefficient } \mu=0.60 \\
& \text { beams size: } 24 \mathrm{in} . \times 28 \mathrm{in} .(610 \mathrm{~mm} \times 711 \mathrm{~mm}) \\
& \text { effective beam spans: } 22 \mathrm{ft} 6 \mathrm{in} .(6.9 \mathrm{~m}) \\
& \text { allowable horiz. shear stress } f_{c v}=1200 \mathrm{psi}(8.3 \mathrm{MPa}) \\
& f_c^{\prime}=5000 \mathrm{psi}, \text { normal weight }(34.5 \mathrm{MPa}) \\
& f_y=f_{y t}=60,000 \mathrm{psi}(414 \mathrm{MPa})
\end{aligned}
$$

Use a Dywidag connector system.

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Problem 4

Design a ductile precast prestressed concrete moment-resistant connection of a ductile frame in a high intensity seismic zone subjected to a factored seismic moment $M_u=1350 \mathrm{ft}$-kip ( $1831 \mathrm{kN}$-m) and a post-yield rotation $\theta_p=2.75$ percent. The frame precast beams have spans of $20^{\prime}-0^{\prime \prime}$ and the clear spans are $17^{\prime}-4^{\prime \prime}(5.3 \mathrm{~m})$. Each story height is $9^{\prime}-0^{\prime \prime}(2.74 \mathrm{~m})$. Use the Dywidag Ductile Connection assembly (DDC) in your solution. Given:
$$
\begin{aligned}
& \text { column sizes: } 38 \mathrm{in} . \times 38 \mathrm{in} .(965 \mathrm{~mm} \times 965 \mathrm{~mm}) \\
& \text { center to center Ductile Rods, }\left(d-d^{\prime}\right): 27 \mathrm{in} .(686 \mathrm{~mm}) \\
& f_c^{\prime}=5000 \mathrm{psi} \text {, normal weight concrete }(34.5 \mathrm{MPa})
\end{aligned}
$$

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Problem 5

Design the moment resisting connection in Problem 13.4 as a hybrid connection using both mild steel and prestressing post-tensioned reinforcement. Given:
$$
\begin{aligned}
f_c^{\prime} & =5000 \mathrm{psi}, \text { normal weight concrete }(34.5 \mathrm{MPa}) \\
f_y & =f_{y t}=60,000 \mathrm{psi}(414 \mathrm{MPa}) \\
f_{p u} & =270,000 \mathrm{psi}(1862 \mathrm{MPa}) \\
f_{p s} & =<0.90 f_{p u} \text { (determine from compatibility analysis) } \\
f_{p e} & =160,000 \mathrm{psi}(1103 \mathrm{MPa}) \\
E_s & =29,000 \mathrm{ksi}(200,000 \mathrm{MPa}) \\
E_{p s} & =28,000 \mathrm{ksi}(193,000 \mathrm{MPa}) \\
f_c & =1000 \mathrm{psi}(6.9 \mathrm{MPa}) \text { maximum concrete stress at post-tensioning }
\end{aligned}
$$

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