**
Powerhouse Design- Miniwatt Hydro
Web Page**

**Design of Powerhouse
Substructure W. Fay P.E.**

**Mini-Watt Electric
Expansion 10/15/88**

**Orange, Massachusetts**

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Stamp**

**I) Methodology:**

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**A) Floor slabs to be designed as
one-way floor slabs using the**

**"ACI-Ultimate Strength Design
Methods"**

** **

**B) Walls to be designed as one-way
floor slabs using the "ACI-Ultimate**

**Strength Design Methods" and
assuming hydrostatic load distributions for**

**saturated soils.**

** **

**C) Beams to be designed using ASI
Code.**

** **

** **

**II) Design Approach:**

** **

**A) Design assumes waterbox floor
slab is supported on three sides by **

**reinforced concrete walls and by a
steel beam on the downstream, **

**tailrace side. Additionally, the
discharge pit will be subdivided into **

**two equal sized compartments by a
wall running in the streamwise **

**direction and this reinforced wall
will support the midspan of the **

**waterbox floor.**

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**Sketch:**

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**B) Waterbox floor slab loads will
considst of uniformly distributed **

**dead loads of water, rebar and
concrete and the point loads of the **

**turbine gate cases. The design
will incorporate four (4) transverse **

**beams, one on each side of the
gate cases to support the gate case **

**point load.**

** **

**C) The discharge pit walls will be
designed for external loads for when **

**the pit may occasionally be
dewatered by a coffer dam to maintain the **

**draft tubes.**

**
(1)**

**D) Waterbox walls will be designed
for the internal pressure due to the **

**headwater and for external
pressure due to dewatering and emergency **

**repair work during highwater.**

**E) Generator floor slabs will be
designed for a uniform floor loading of**

**250 lb/sq.ft and for the point
loads of the generator, turbine shaft,**

**turbine runner and hydraulic
thrust. This point load will be supported **

**by transverse beams similiar to B)
above. These beams will be designed **

**according to ASI Code to have
proper strength, with minimal deflection.**

** **

**F) The upstream side of the
generating floor will be supported by a **

**steel beam spanning the waterbox
inlets.**

** **

**G) The waterbox will be divided
into two (2) seperate chambers by a **

**structural wall.**

** **

**H) The main steel beam supporting
the waterbox floor slab will be**

**designed conservatively to support
the weight of the waterbox rear wall,**

**powerhouse rear wall and one half
(1/2) the weights of the waterbox**

**floor slab, the generating room
floor slab, the turbine/generator**

**hydraulic thrust point load and
the overhead crane point load (assumed**

**to be in the most compromising
position).**

** **

**I) The main steel beam supporting
the generating room floor slab and**

**spanning the waterbox inlets will
be designed conservatively to support**

**the weight of the generating room
upstream wall and one half (1/2) the**

**weights of the generating room
floor slab, the turbine/generator**

**hydraulic thrust point load and
the overhead crane point load (assumed**

**to be in the most compromising
position).**

** **

**J) The following elevations will
be assumed:**

** **

******(Datum is USGS-MSL)******

** **

**1) Top of discharge pit floor slab
- 476.3 msl**

** **

**2) Mean tailwater elevation -
490.0 msl**

** **

**3) Waterbox floor - 493.3 msl**

** **

**4) Mean headwater elevation -
501.3 msl**

**5) Top of generating room floor
slab - 522.0 msl**

** **

**Assume main beams forming the
discharge pit/tailrace and water box inlet**

**arches are surplus from the Route
2 bridge rebuild (WF-30"x 124 #/ft).**

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**
(2)**

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**III) Design of the Waterbox Floor
Slab:**

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**A) Dimensions- from Bruce Dexter
layout dated 8/22/88 entitled "Lower**

**Walls etc". Assume these
dimensions are correct.**

** **

**1) External dimensions:**

** **

**a) length = 173" + 173" + 3*(24")
= 418" = 34' 10" = 34.83'**

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**b) width = 18'**

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**2) Internal dimensions:**

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**a) length = 30.83'**

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**b) width = 14.0'**

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**B) Loading:**

** **

**1) Water, total load = 62.4 #/ft3
* (14'* (501.3-493.3)**

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** = 215,465 lbs**

** **

**2) Water, load per foot width of
box = 1575 lbs/ft-width of flume**

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**3) Water, load per foot width of
box per foot width of beam = 499 lb/ft**

** **

**4) Concrete, total load = 150
#/ft3 * 14' * 30.83'***

** **

**
(9"/(12"/ft)) = 48,557 lbf**

** **

**5) Concrete, load per foot width
of box = 48,557 lbf/30.83' = 1575 **

**
lbf/ft width of box**

** **

**6) Concrete, load per foot width
of box per foot width of beam = **

** **

** 1575 lbf/ft-width/14' = 113
lbf/ ft**

** **

**7) Since the waterbox will be
periodically dewatered, treat the water **

**as a live distributed load and use
the larger live load overload factor **

**ACI ultimate strength multipliers.**

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**C) Sketch of typical section
through proposed waterbox floor:**

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**
(3)**

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**D) Design Calculations: -
reference, "Design of Concrete Structures", **

**9th ed., Winter & Nilson.**

** **

**1) Assume the yield strength of
the steel reinforcing is 30,000 psi and **

**that the compressive strength of
the concrete is 3000 psi.**

** **

**2) Select the trial thickness of
the slab, use L/20 from Table 5.1,**

**p.206 in Winter & Nilson.**

** **

**T= (12 "/ft * 14')/20 = 8.4"
approximately = 9"**

** **

**3) The slab weight is 150 #/ft3 *
(9/12) = 113 PSF**

** **

**4) Apply the ACI load multipliers
and obtain the factored load:**

** **

**Dead Load = 113 PSF * 1.4 = 158.2
PSF**

** **

**Live Load = 499 PSF * 1.7 = 848.3
PSF**

** **

**Total Factored Load = 1007 PSF**

** **

**5) Use the ACI moment coefficients
to determine the design moments at**

**the critical sections:**

** **

**a) Since the floor slab is being
designed as a one-way slab in the**

**short direction (ie: from the
inlet end to the tailrace end), the slab**

**will be resting on the main 30"
beam which acts as the arch at the**

**rear of the poerhouse over the
tailrace and will be built into the top**

**of the rear (upstream wall) of the
discharge pit. At the tailrace end,**

**the floor slab is simply supported
and the beam is free to twist and**

**cannot be assumed to be rigid, so
use:**

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**(1/11)*Wu*ln^2 >>>>>>>>from Table
8.1 W&N**

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**Sketch:**

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**b) At the upstream end, the slab
is to be built into the discharge pit**

**wall and can be assumed to be
rigid, so use:**

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**(1/14)*Wu*ln^2>>>>>>>>from Table
8.1 W&N**

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**Sketch:**

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**
(4)**

**c) At the interior span use:**

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**(1/14)*Wu*ln^2>>>>>>>>from Table
8.1 W&N**

**d) At the tailrace: -M = 1/11*1.01
KSF *14'^2 = 18.0 ft-kips**

** **

**e) At the upstream end: -M =
1/14*1.01 KSF *14'^2 = 14.0 ft-kips**

** **

**d) At the midspan: -M = 1/16*1.01
KSF *14'^2 = 12.4 ft-kips**

** **

**5) Determine the maximum steel
ratio permitted by the ACI Code:**

** **

**Pmax = 0.75*Pbalanced =
0.75*0.85*B1*(fc'/fy)*(87,000/(87,000+fc'))**

** **

**this formula for fc'<4000 psi and
B1=0.85**

** **

**Pmax=0.75*0.85*0.85*(3000
psi/30,000 psi)*(87,000/(87,000 + 30,000))**

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** = 0.04**

** **

**6) Determine the minimum required
effective depth: (This is controlled**

**by the largest moment at the
tailrace)**

** **

**d^2 =
Mu/(phi*p*fy*b*(1-(0.59*p*fy/fc))) note: phi=0.9 for bending**

** **

** = (18
ft-kips*(12"\ft))/(0.9*0.04*30*12*(1-.59*0.04*(30,000/3000)))**

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** = 21.8 in^2**

** **

**Therefore, d = 4.7 inchs**

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**7) Determine the minimum effective
depth using code restrictions:**

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**dm= 9"- 1" = 8"**

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**8) Since the calculated value of
4.7 inches is less then the coded**

**effective depth, use d= 9 inches**

** **

**9) At the tailrace end, assume the
stress block depth a = 1.00 inch.**

**Then the area of steel required
per foot width in the top of the slab**

**is:**

** **

**As= Mu/(phi*fy*(d-a/2))= (18
ft-kips*12"/ft)/0.9*30*(8-1/2)= 1.06 in^2**

** **

**10) Check the assumed depth:**

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**a= As*fy/(0.85*fc'*b)= 1.06 in^2
*30,000/(0.85*3000*12"/ft)= 1.04 in^2**

** **

**11) The assumed area of steel and
the calculated area of steel are**

**reasonably close so use 1.06 in^2
of rebar per foot width of floor slab.**

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**
(5)**

**12) At the other critical sections
use the same lever arm to determine**

**the required cross sectional areas
of steel rebar:**

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**a) at the midspan: As= 12.4 ksi*12/(0.9*30*(8-1/2))=
0.73 in^2**

** **

**b) at the upstream wall: As= 14
ksi*12/(0.9*30*(8-1/2))= 0.83 in^2**

** **

**13) The minimum reinforcement
required to control shrinkage is: see p. **

**207, W&N.**

** **

**As= 0.002*12*9= 0.216 in^2/ 12"
with strip**

** **

**The required steel necessary for
shrinkage is met by the steel required **

**to meet the externally applied
loads.**

** **

**14) Determine the factored shear
force:**

** **

**Vu= 1.15 *
(1007*14/2)-1007*(8.5/12)= 8106-713 = 7393 lbs**

** **

**15) The nominal shear strength of
the slab is:**

** **

**Vn= Vc= 2*b*d*fc'^0.5**

** **

** = 2*12*8.5*(3000 psi^0.5)**

** **

** = 11,173 lbs**

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**16) The design shear strength is:**

** **

** phi*Vc= 0.85*11,173 lbs= 9,498
lbs**

** **

**17) Since the design shear
strength is above the required shear strength**

**by 30 %, no additional steel is
necessary to resist the internal shear**

**forces.**

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** **

**IV) Design the Steel Main Support
Beam at the Tailrace**

** **

**A) Data for Bridge Beam:**

** **

**1) height= 30"**

** weight= 124 lbs/ft-width**

** length= 55 feet**

** section modulus= 355 in^3**

** moment of inertia= 5360 in^4**

** depth= 30.16"**

** width= 10.521"**

** flange thickness= 0.93"**

** web= 0.585"**

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**2) Flat of flange=
(10.521"-0.585")/2= 4.97"**

** 90 % of the flat is 4.5"**

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**
(6)**

**B) Determine the Beam Loading:**

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**1) Point Loads:**

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**a) generator= 225 rpm, 32 pole,
197 kva= 15,800 lbs**

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**b) exciter= 1400 lbs**

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**c) Shipping weight of turbine=
14,000 lbs**

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**2) Crane Load - assume a point
load in the middle of the beam of 5 tons **

**for a five ton bridge crane, this
gives a 2.0 safety factor on the **

**crane load.**

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**3) Dead Loads:**

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**a) Powerhouse backwall:**

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**((31'*(522.0-506.0)*0.75) +
((506.0-492.0)*1.0))*150 lbs/ft^3= 93,000 #**

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**b) Waterbox floor:**

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**(18'*31'*1')*150 lbs/ft^3= 83,700
#**

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**c) Generating room floor:**

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**(18'*31'*1')*150 lbs/ft^3= 83,700
#**

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**d) Water:**

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**18'*31'*(504.0-493.0)*62.4
lbs/ft^3= 383,011 lbs**

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**4) Total Distributed Load:**

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**(93,000 # + 83,700 #/2 + 383,011
#/2)/31'= 18,000 lbs/ft-width beam**

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**5) Total point load is:**

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**(15,800 # + 1400 # + 14,000 # )/2
+ 5000 #= 20,600 lbs**

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**6) Sketch the beam and the loading
diagram:**

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**
(7)**

**C) Determine the extreme fiber
stress and the maximum deflection:**

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**1) Even though the beam will be
embedded into the walls on either side, **

**the weight of the wall immediately
above the beam will not counter act **

**the loading and one should assume
that the beam is simply supported. **

**This is a conservative assumption
and will result in the largest **

**moment.**

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**2) Maximun Moment:**

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**6.8' * 20,600 lbs + 18,000 lb/ft *
(13.5'^2)/8 = 550,142 ft-lbs**

** **

**3) The extreme fiber stress is:**

** **

**Sigma = M/Z = (550,142 ft-lbs *
12"/ft)/355 in^3 = 18,596 psi**

** **

**4) From the AISC "Manual of Steel
Construction", 7th edition, P. 5-124, **

**section 1.5.1.4.1, the allowable
bending stress for W shapes is **

**0.66*Fy, where Fy is 36,000 psi.**

** **

**Therefore, the recommended maximum
load is: **

**Sigma max= 0.66*36,000 psi= 23,760
psi <<<<<<<<*******

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**15) Since the calculated stress is
less then the maximum recommended by **

**AISC Code, the 30" beam is alright
for strength.**

** **

**16) Determine the maximum
deflection:**

** **

**a) For uniformly distributed load:**

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**delta max= 5*w*l^4/(384*E*I)**

** **

** = 5* 18,000 lb/ft *
(13.5'*12")^4/(384*29,000,000 psi* 5360 **

** in^4*12)= 0.09 inch**

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**b) For the point load:**

** **

**delta max= p*l^3/(48*E*I)**

** **

** = 20,600 lbs *
13.5'*12"/ft)^3/(48*29,000,00 psi*5360 in^4)**

** = 0.01 inch**

** **

**c) Total defltion is the
superposition of the deflections due to the **

**two different types of loads and
is**

** **

**0.09" + 0.01" =0.1"**

** **

**17) The calculated deflection is
negligible and should not effect the**

**concrete resting upon the beam,
especially since the major deflection**

**will take place when the concrete
is wet, before it dries.**

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**
(8)**

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**V) Design the turbine gate case
support beams:**

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**A) Sketch the design:**

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**
Plan View**

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**B) Sketch the beam loading:**

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**C) Determine the beam size:**

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**1) Size the beam at 80 % of the
AISC Codes maximum allowable stress or**

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**0.8 * 21,600 psi= 17,280 psi**

** **

**2) Maximum moment is 7' * 3500 # =
24,500 ft-lbs**

** **

**3) Z= M/sigma= (24,500 ft-lbs * 12
in/ft)/17,280 psi= 17 in^3**

** **

**D) From the AISC Handbook, 7th
ed., P. 1-42, tentatively choose a**

**W8"x20 lbs/ft**

** **

**E) Beam Properties:**

** **

** height= 8.14"**

** weight= 20 lbs/ft-width**

** length= 18 feet**

** section modulus= 17 in^3**

** moment of inertia= 69.4 in^4**

** depth= 8.14"**

** width= 5.268"**

** flange thickness= 0.378"**

** web= 0.248"**

**
(9)**

**F) Check the deflection:**

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**Sigma max= P*L^3/(48*E*I)= 3500# *
(14'*(12"/ft)^3)/(48 * 29,000,000 psi**

*** 69.4 in^3= 0.17 inch <<<< okay**

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**The choosen beam will meet the
design requirements.**

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**VI) Design the generator support
beams:**

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**A) Sketch the design:**

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Plan View**

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**B) Sketch the beam loading:
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**C) Determine the beam size:**

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**1) Size the beam at 80 % of the
AISC Codes maximum allowable stress or**

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**0.8 * 21,600 psi= 17,280 psi**

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**2) Maximum moment is 7' * 17,600 #
= 123,200 ft-lbs**

** **

**3) Z= M/sigma= (123,200 ft-lbs *
12 in/ft)/17,280 psi= 86 in^3**

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**D) From the AISC Handbook, 7th
ed., P. 1-42, tentatively choose a**

**W10"x77 lbs/ft
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**
(10)**

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**E) Beam Properties:**

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** height= 10.62"**

** weight= 77 lbs/ft-width**

** length= 18 feet**

** section modulus= 86.1 in^3**

** moment of inertia= 457 in^4**

** depth= 10.62"**

** width= 10.2"**

** flange thickness= 0.868"**

** web= 0.535"**

**
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**F) Check the deflection:**

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**Sigma max= P*L^3/(48*E*I)= 17,600#
* (14'*(12"/ft)^3)/(48 * 29,000,000**

**psi * 86.1 in^3= 0.7 inch <<<<
okay**

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**The choosen beam will meet the
design requirements.**

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** **

**VII) Design the generator floor:**

** **

**A) Dimensions- from Bruce Dexter
layout dated 8/22/88 entitled "Lower**

**Walls etc". Assume these
dimensions are correct. Assume the T/G set is **

**supported by 10" WF beams. Design
the floor for 300 lbs/ft live load, **

**plus the dead load of the
concrete.**

** **

**1) External dimensions:**

** **

**a) length = 173" + 173" + 3*(24")
= 418" = 34' 10" = 34.83'**

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**b) width = 18'**

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**2) Internal dimensions:**

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**a) length = 30.83'**

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**b) width = 14.0'**

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**B) Loading:**

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**1) Concrete, total load = 150
#/ft3 * 14' * 30.83'***

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**
(9"/(12"/ft)) = 48,557 lbf**

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**2) Concrete, load per foot width
of box = 48,557 lbf/30.83' = 1575**

**lbf/ft width of box**

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**3) Concrete, load per foot width
of box per foot width of beam =**

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** 1575 lbf/ft-width/14' = 113
lbf/ ft**

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**
(11)**

**C) Sketch of typical section
through proposed waterbox floor:**

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**D) Design Calculations: -
reference, "Design of Concrete Structures",**

**9th ed., Winter & Nilson.**

** **

**1) Assume the yield strength of
the steel reinforcing is 30,000 psi and**

**that the compressive strength of
the concrete is 3000 psi.**

** **

**2) Select the trial thickness of
the slab, use L/20 from Table 5.1,**

**p.206 in Winter & Nilson.**

** **

**T= (12 "/ft * 14')/20 = 8.4"
approximately = 9"**

** **

**3) The slab weight is 150 #/ft3 *
(9/12) = 113 PSF**

** **

**4) Apply the ACI load multipliers
and obtain the factored load:**

** **

**Dead Load = 113 PSF * 1.4 = 158.2
PSF**

** **

**Live Load = 300 PSF * 1.7 = 510.0
PSF**

** **

**Total Factored Load = 668 PSF**

** **

**5) Use the ACI moment coefficients
to determine the design moments at**

**the critical sections:**

** **

** a) Since the floor slab is being
designed as a one-way slab in the**

**short direction (ie: from the
inlet end to the tailrace end), the slab**

**will be resting on the main 30"
beam which acts as the arch at the**

**front of the powerhouse, over the
inlets and will be built into the top**

**of the rear (downstream wall) of
the water boxes. At the inlet end, the**

**floor slab is simply supported and
the beam is free to twist and cannot**

**be assumed to be rigid, so use:**

** **

** (1/11)*Wu*ln^2 >>>>>>>>from Table
8.1 W&N**

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**Sketch:**

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**
(12)**

**b) At the upstream end, the slab
is to be built into the discharge pit**

**wall and can be assumed to be
rigid, so use:**

** **

**(1/14)*Wu*ln^2>>>>>>>>from Table
8.1 W&N**

** **

**Sketch:**

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**c) At the interior span use:**

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**(1/16)*Wu*ln^2>>>>>>>>from Table
8.1 W&N**

**d) At the inlets: -M = 1/11*0.668
KSF *14'^2 = 11.9 ft-kips**

** **

**e) At the downstream end: -M =
1/14*0.668 KSF *14'^2 = 9.35 ft-kips**

** **

**f) At the midspan: -M = 1/16*0.668
KSF *14'^2 = 8.18 ft-kips**

** **

**5) Determine the maximum steel
ratio permitted by the ACI Code:**

** **

**Pmax = 0.75*Pbalanced =
0.75*0.85*B1*(fc'/fy)*(87,000/(87,000+fc'))**

** **

**this formula for fc'<4000 psi and
B1=0.85**

** **

**Pmax=0.75*0.85*0.85*(3000
psi/30,000 psi)*(87,000/(87,000 + 30,000))**

** **

** = 0.04**

** **

**6) Determine the minimum required
effective depth: (This is controlled**

**by the largest moment at the inlet
end)**

** **

**d^2 =
Mu/(phi*p*fy*b*(1-(0.59*p*fy/fc))) note: phi=0.9 for bending**

** **

** =
(11.9ft-kips*(12"\ft))/(0.9*0.04*30*12*(1-.59*0.04*(30,000/3000)))**

** **

** = 14.43 in^2**

** **

**Therefore, d = 3.8 inchs**

** **

**7) Determine the minimum effective
depth using code restrictions:**

** **

**dm= 9"- 1" = 8"**

** **

**8) Since the calculated value of
4.7 inches is less then the coded**

**effective depth, use d= 9 inches**

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**
(13)**

**9) At the tailrace end, assume the
stress block depth a = 1.00 inch.**

**Then the area of steel required
per foot width in the top of the slab**

**is:**

** **

**As= Mu/(phi*fy*(d-a/2))= (11.9
ft-kips*12"/ft)/0.9*30*(8-1/2)= 0.62 in^2**

** **

**10) Check the assumed depth:**

** **

**a= As*fy/(0.85*fc'*b)= 0.62 in^2
*30,000/(0.85*3000*12"/ft)= 0.61 in**

** **

**11) Reiterate assuming a=0.61 in:**

** **

**As=Mu/(phi*f*(d-a/2))=(11.9
ft-kips*12"/ft)/0.9*30*(8-0.61/2)= 0.69 in^2**

** **

**12) Reiterate assuming As=0.69
in^2:**

** **

**a= As*fy/(0.85*fc'*b)= 0.69 in^2
*30,000/(0.85*3000*12"/ft)= 0.68 in**

** **

**13) Reiterate assuming a=0.68 in:**

** **

**As=Mu/(phi*f*(d-a/2))=(11.9
ft-kips*12"/ft)/0.9*30*(8-0.68/2)= 0.69 in^2**

** **

** **

** **

**14) The assumed area of steel and
the calculated area of steel are**

**reasonably close so use 0.69 in^2
of rebar per foot width of floor slab.**

** **

**15) At the other critical sections
use the same lever arm to determine**

**the required cross sectional areas
of steel rebar:**

** **

**a) at the midspan: As= 8.18
ksi*12/(0.9*30*(8-1/2))= 0.48 in^2**

** **

**b) at the upstream wall: As= 9.35
ksi*12/(0.9*30*(8-1/2))= 0.55 in^2**

** **

**16) The minimum reinforcement
required to control shrinkage is: see p.**

**207, W&N.**

** **

**As= 0.002*12*9= 0.216 in^2/ 12"
with strip**

** **

**The required steel necessary for
shrinkage is met by the steel required**

**to meet the externally applied
loads.**

** **

**17) Determine the factored shear
force:**

** **

**Vu= .668 *
(1007*14/2)-1007*(8.5/12)= 8106-713 = 4294 lbs**

** **

**15) The nominal shear strength of
the slab is:**

** **

**Vn= Vc= 2*b*d*fc'^0.5**

** **

** = 2*12*8.5*(3000 psi^0.5)**

** **

** = 11,173 lbs**

** **

** **

**
(14)**

**16) The design shear strength is:**

** **

** phi*Vc= 0.85*11,173 lbs= 9,498
lbs**

** **

**17) Since the design shear
strength is above the required shear strength**

**by 60 %, no additional steel is
necessary to resist the internal shear**

**forces.**

** **

** **

**VIII Design Waterbox Walls:**

** **

**A) Dimensions- from Bruce Dexter
layout dated 8/22/88 entitled "Lower**

**Walls etc". Assume these
dimensions are correct. Note, these rear **

**walls are not designed as axial
bearing members. They are only designed **

**as panels to take the water
pressure.**

** **

**1) External dimensions:**

** **

**a) height= 14'**

** **

**b) width = 14'**

** **

**2) Internal dimensions:**

** **

**a) length = 14'**

** **

**b) width = 14.0'**

** **

**B) Loading:**

** **

**1) Concrete, total load = 150
#/ft3 * 14' * 14'* (9"/(12"/ft)) =**

** 22,050 lbf**

** **

**2) Concrete, load per sq. ft. =
48,557 lbf/30.83' = 113 lbf/ft^2**

** **

**3) Water Load= 62.4 lbf/ft^3 * 14'
wide * 14' deep * 1' thick/ 14'wide**

** = 873 PSF. This is
the maximum load at the base of the**

** hydrostatic load.**

** **

**
**

**C) Sketch of typical section
through proposed waterbox floor:**

** **

** **

** **

** **

** **

** **

** **

** **

** **

**
**

** **

** **

** **

** **

**
(15)**

**D) Design Calculations: -
reference, "Design of Concrete Structures",**

**9th ed., Winter & Nilson.**

** **

**1) Assume the yield strength of
the steel reinforcing is 30,000 psi and**

**that the compressive strength of
the concrete is 3000 psi.**

** **

**2) Select the trial thickness of
the slab, use L/20 from Table 5.1,**

**p.206 in Winter & Nilson.**

** **

**T= (12 "/ft * 14')/20 = 8.4"
approximately = 9"**

** **

**3) The slab weight is 150 #/ft3 *
(9/12) = 113 PSF**

** **

**4) Apply the ACI load multipliers
and obtain the factored load:**

** **

**Dead Load = 113 PSF * 1.4 = 158.2
PSF**

** **

**Live Load = 873 PSF * 1.7 = 1484.0
PSF**

** **

**Total Factored Load = 1643 PSF**

** **

**5) Use the ACI moment coefficients
to determine the design moments at**

**the critical sections:**

** **

** a)The wall is rigidly built into
the floor slabs at the top and **

**bottom, so use:**

** **

** (1/14)*Wu*ln^2 >>>>>>>>from Table
8.1 W&N**

** **

**Sketch:**

** **

** **

** **

** **

** **

** **

** **

**
**

** **

**b) At the interior span use:**

** **

**(1/16)*Wu*ln^2>>>>>>>>from Table
8.1 W&N**

** **

**c) At the top: -M = 1/14*1.643 KSF
*14'^2 = 23.0 ft-kips**

** **

**d) At the bottom: -M = 1/14*1.643
KSF *14'^2 = 23.0 ft-kips**

** **

**e) At the midspan: -M = 1/16*1.643
KSF *14'^2 = 23.0 ft-kips**

** **

**5) Determine the maximum steel
ratio permitted by the ACI Code:**

** **

**Pmax = 0.75*Pbalanced =
0.75*0.85*B1*(fc'/fy)*(87,000/(87,000+fc'))**

** **

**this formula for fc'<4000 psi and
B1=0.85**

** **

**
(16)**

**Pmax=0.75*0.85*0.85*(3000
psi/30,000 psi)*(87,000/(87,000 + 30,000))**

** **

** = 0.04**

** **

**6) Determine the minimum required
effective depth: (This is controlled**

**by the largest moment at either
the top or the bottom)**

** **

**d^2 =
Mu/(phi*p*fy*b*(1-(0.59*p*fy/fc))) note: phi=0.9 for bending**

** **

** = (23
ft-kips*(12"\ft))/(0.9*0.04*30*12*(1-.59*0.04*(30,000/3000)))**

** **

** = 27.9 in^2**

** **

**Therefore, d = 5.3 inchs**

** **

**7) Determine the minimum effective
depth using code restrictions:**

** **

**dm= 9"- 1" = 8"**

** **

**8) Since the calculated value of
5.3 inches is less then the coded**

**effective depth, use d= 8 inches**

** **

**9) At the tailrace end, assume the
stress block depth a = 1.00 inch.**

**Then the area of steel required
per foot width in the top of the slab**

**is:**

** **

**As= Mu/(phi*fy*(d-a/2))= (23
ft-kips*12"/ft)/0.9*30*(8-1/2)= 1.36 in^2**

** **

**10) Check the assumed depth:**

** **

**a= As*fy/(0.85*fc'*b)= 1.36 in^2
*30,000/(0.85*3000*12"/ft)= 1.33 in**

** **

**11) Reiterate assuming a=1.33 in:**

** **

**As=Mu/(phi*f*(d-a/2))=(23
ft-kips*12"/ft)/0.9*30*(8-1.33/2)= 1.39 in^2**

** **

**12) Reiterate assuming As=1.39
in^2:**

** **

**a= As*fy/(0.85*fc'*b)= 1.39 in^2
*30,000/(0.85*3000*12"/ft)= 1.37 in**

** **

**13) Reiterate assuming a=1.37 in:**

** **

**As=Mu/(phi*f*(d-a/2))=(23
ft-kips*12"/ft)/0.9*30*(8-1.37/2)= 1.40 in^2**

** **

**14) The assumed area of steel and
the calculated area of steel are**

**reasonably close so use 0.69 in^2
of rebar per foot width of floor slab.**

** **

**15) At the other critical sections
use the same lever arm to determine**

**the required cross sectional areas
of steel rebar:**

** **

**a) at the midspan: As= 23
ksi*12/(0.9*30*(8-1.37/2))= 1.40 in^2**

** **

**b) at the bottom: As= 23
ksi*12/(0.9*30*(8-1.37/2))= 1.40 in^2**

** **

** **

**
(17)**

**16) The minimum reinforcement
required to control shrinkage is: see p.**

**207, W&N.**

** **

**As= 0.002*12*9= 0.216 in^2/ 12"
with strip**

** **

**The required steel necessary for
shrinkage is met by the steel required**

**to meet the externally applied
loads.**

** **

**17) Determine the factored shear
force: Note that the dead weight of **

**the vertical concrete does not add
to the shear component.**

** **

**Vu=1.15*1484*14/2-1484*(9.0/12)=
11,946-1113 = 10833 lbs**

** **

**15) The nominal shear strength of
the slab is:**

** **

**Vn= Vc= 2*b*d*fc'^0.5**

** **

** = 2*12*9.0*(3000 psi^0.5)**

** **

** = 11,831 lbs**

** **

**16) The design shear strength is:**

** **

** phi*Vc= 0.85*11,173 lbs= 9,498
lbs**

** **

**17) The design shear strength is
slightly less then the required shear**

**strength.However, the differential
is small and no additional steel is**

**necessary to resist the internal
shear forces.**

** **

**18) Use 1.4 in^2 of steel for the
vertical reinforcement.**

** **

**IX) Design the discharge pit
walls:**

** **

**A) Assume the pit is dewatered and
drained externally. The height of**

**water is 490.0-476.0=14'**

** **

**B) This design is identical to the
waterbox walls.**

** **

**C) Use 1.4 in^2 of steel per foot
width of wall.**

** **

**X) Design main 30" beam support
column:**

** **

**A) Determine the load on the
column:**

** **

**1) Sketch the freebody diagram:**

** **

** **

** **

** **

** **

** **

** **

** **

** **

**
(18)**

**Ra=((20,600 lbs + (18,000*15'))/2
= 145,300 lbf**

** **

**2) the factored ACI Code load is:**

** **

**Pu=(1.4*(1.4*(18,000 lbf * 15')/2)
+ (1.7 * 20,600/2)**

** **

** = 189,000 lbf + 17,510 lbf =
206,510 lbf**

** **

**B) Determine the nominal axial
load strength of the column, Po, **

**assuming minimal eccentricity:**

** **

**1) Po= 0.85 * fc' * Aconc + fy *
Ast**

** **

**2) By ACI Code, the ratio of the
longitudinal steel area to the gross **

**column area must be:**

** **

**0.01 <= Pg <= 0.08. Try 0.025 to
start.**

** **

**3) Assume the column is 12"
square, built into the discharge pit walls **

**and has a steel plate between the
WF beam flange and the concrete to **

**transmit the load.**

** **

**4) The gross area of the column,
Ag = 144 sq. in.**

** **

**5) Areas of steel are:**

** **

**Ast = Pg * Ag = 0.025 * 144 in.
sq. = 3.6 in. sq.**

** **

**6) Po = 144 in. sq. *
(0.85*(1-0.025) * 3000 psi + 30,000 psi * 0.025**

** **

** = 466,020 lbf**

** **

**C) Determine the ACI factored
design strength:**

** **

**Pdesign = phi*Po = 0.80 * 0.70 *
Po**

** **

** = 0.8 * 0.7 * 466,020 lbf**

** **

** = 260,971 lbf**

** **

**D) Since the factored ACI design
strength is greater then the factored **

**ACI load, this design will work**

** **

**phi * Po > Pu >>>>>>>>>>>> 260,971
lbf > 206,510 lbf**

** **

**E) Determine the number of bars
and their size:**

** **

**1) Assume six bar design**

** **

**2) Area of single bar = Ast/# bars**

** **

** = 3.6 in^2/6
= 0.60 sq. in.**

** **

**3) From ASTM rebar, table #7 bars
are 0.6 in. sq.**

** **

**
(19)**

**F) Sketch design:**

** **

** **

** **

** **

** **

** **

** **

** **

** **

** **

** **

**1) minimum spacing is 1.5 * 0.875
= 1.31"**

** **

**2) minimum tie wire size is #4**

** **

**3) concrete cover must be 1 1/2"
thick**

** **

**4) every corner to be supported by
a tie wire**

** **

**5) tie wire spacing shall be every
14" of column rise**

** **

** **

** **

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** **

** **

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** **

** **

** **

** **

** **

**G) Check the slenderness ratio of
the column:**

** **

**1) SR = K*Lu/r =
K*Lu/0.3*W K = 1 for unbraced columns**

**
Lu = 492.3 - 476.3 = 16'**

**
w = 12"**

** SR = 1 * 16'/(0.3*1') = 53**

** **

**Since 53>22 this design is slender**

** **

**2) Determine w for SR= 22 minimum**

** **

**W = KLu/(0.3*SR) = 16'/(0.3*22) =
2.42' = 30"**

** **

**H) Retrofit design so that wall is
30" thick for the 12" length of the **

**wall which the column is embedded
into.**

** **

** **

** **

** **

** **

** **

** **

**
(20)**

**I) Sketch design:**

** **

** **

** **

** **

** **

** **

** **

** **

** **

** **

** **

** **

**XI) Check the rock foundation
bearing capacity:**

** **

**A) Total weight of the powerhouse
and equipment:**

** **

**Water + 2 floors + machinery +
back & front wall + side walls =**

** **

**215,465 lbf + 100,000 lbf + 36,200
lbf + 186,000 lbf + 93,000 lbf =**

** **

**630,665 lbf**

** **

**B) Total surface bearing area is:**

** **

**(34.83' + 2*18') * 1' = 71 sq. ft.**

** **

** **

**C) The stress on the rock is:**

** **

**630,665 lbf/71 sq. ft. = 8900
lbf/ft^2 = 4.45 tons/sq. ft.**

** **

**D) "American Civil Engineer's
Handbook", Merriman & Wiggin, 5th edition,**

**P. 711, table lists the allowable
soil pressures in short tons per sq.**

**ft. for very hard native bedrock
at 15 tons/sq.ft.. A short ton is 2000**

**lbs. Since the calculated pressure
of 4.5 tons/sq.ft. is much less then**

**15 tons/sq.ft. This design should
be all right if the walls are poured**

**directly on the rock excavation.
The footing should be chipped square**

**and level before the forms are set
up.**

** **

**XII) Rebar size and spacing
selection:**

** **

**A) Waterbox Floor:**

** **

**1) To obtain 1.06 in. sq./ft.
width slab, use one #7 bar every six**

**inches.**

** **

**2) Use #5 bar at 18 inch spacing
in the longitudinal spacing.**

** **

**B) Generating Room Floor:**

** **

**1) To obtain 0.48 in. sq./ft.
width slab, use one #7 bar every 12**

**inches.**

** **

** **

**
(21)**

**2) Use #5 bar at 18 inch spacing
in the longitudinal spacing.**

** **

**C) Walls:**

** **

**1) To obtain 1.40 in. sq./ft.
width slab, use one #7 bar every 6**

**inches.**

** **

**2) Use #5 bar at 12 inch spacing
in the longitudinal spacing.**

** **

** **

** **