U. S. Department of Agriculture Soil Conservation Service Engineering Division Technical Release Design Unit April 1, 1965 STRUCTURAL DESIGN OF STANDARDCOVEREDRISERS No. 30 PFUXFACE This Technical Release presents the criteria and procedures established for the structursl design and detailing of Standard Covered Risers. Various criteria and proportions of drop inlet spillways were selected at a meeting of the "Subcommittee on Standard Structural Details" held in Spartanburg, South Carolina, during October 23-27, 1961. Additional criteria, together with procedures for the structural design of Standard Covered Risers, developed as a result of the Subcommittee's meeting were reviewed at a meeting of Engineering and Watershed Planning Unit Design Engineers held in Washington, D. C., during May 20-24, 1963. A revised edition of "Criteria end Procedures for the Structural Design dated April 1, 1964, was then sent to the of Standard Covered Risers", Engineering and Watershed Planning Unit Design Engineers for their use, Release is an outgrowth of the prereview and comment. This Technical ceding meetings and reviews. Criteria and procedures used in the preparation of standards should be selected to insure applicability to the widest practical range of site This philosophy was used in preparing this Technical conditions. Much of the material contained herein either applies directly, Release. or may be adapted readily, to risers of types other than the Standard Covered Risers. Mr. Edwin S. Ailing developed most of the procedures for structural This Technical Release was prepared by design presented herein. Mr. Ailing and other personnel of the Design Unit, Design Branch, Engineering Division at Hyattsville, Maryland. I - i TECHNICAL RELEASE NUMBER 30 STRUCTURAL DESIGN OF STANDARD COVEREDRISERS Contents Page PREFACE NOMENCLATURE CHAFTERl. CRITERIA Standard Proportions, Details, and Data Limitations on the Use of the Standard Plans Riser Heights Pipe Velocities Ice Conditions Allowable Stresses and Bearing Pressures Concrete Reinforcing Steel Earth Bearing Pressures Loads Loads on Riser Walls Lateral soil pressures Water pressures during pipe flow Composite wall pressure diagram for design Loads on Cover Slab Embankment Load on Riser Wind Flotation Criteria Location of Construction Joints in Riser Walls cm 2. l-l l-l l-l l-l l-l l-2 l-2 l-2 l-2 l-2 l-2 l-2 l-3 l-4 l-5 l-5 1-6 1-6 1-6 METHODSOF ANAIYSIS AND DESIGN PROCEDURES Cover Slab Walls Cover Slab Riser Walls, Horizontal Bending Closed Sections Equilibrium relations Analysis for corner moments, Q Members are prismatic Members are non-prismatic Design approach Considerations Direct design by charts Wall thickness and steel selection Sections at Low Stage Inlet(s) 2-l 2-l 2-3 2-3 2-3 2-5 2-5 2-8 2-10 2-10 2-11 2-15 2-15 ii Page Contents 2-15 Sections at the Conduit Entrance Riser Walls, Vertical Bending Wall-to-Footing Connection Verticti flexure in sidewalls Vertical flexure in endwalls Evaluation of coefficients Ky Example of computation of MvC and VVC Wall thickness by shear due to vertical bending Vertical steel Division of wall loading Well Thickness Change Locations Provision for Moment from Embankment Loading At closed sections At conduit entrance Stability Analyses Riser in the Reservoir Area Riser in the Embankment Footing Strength Design CHAPTER 3. 4 2-18 2-18 2-18 2-21 2-22 2-26 2-27 2-27 2-27 2-28 2-28 2-28 2-29 2-30 2-31 2-32 2-32 EXAMPLE DESIGN 3-l 3-l Riser Data Cover Slab and Cover Slab Walls Riser Wall Loading Design of Riser Walls Wall Thickness at Wall-to-Footing Connection Design for Horizontal Bending Vertical Steel at Wall-to-Footing Connection Vertical Steel for Moment from Embankment Loading Stability Analyses Preliminaries Analyses Footing Strength Design Projection Loadings Design Example Plans ;:; 4 ;I; z-87 318 3 -10 3-12 3 -12 3 -12 3-14 Figures Figure Figure Figure l-l l-2 Figure Figure Figure Figure Figure Figure 2-l 2-2 2-3 2-4 2-5 l-3 2-6 Water pressures on riser walls during pipe Representation of heads during pipe flow. Composite wall pressure diagram for design standard X%SerS (vb(-.) = 30 fPS). flow. of Definition sketch of cover slab, Cover slab and cover slab wall steel layout. Definition sketch for horizontal bending. Shear distribution assumed by usual theory. Assumed variation in moment of inertia. Typical direct design chart for co in horizontal bending I) l-3 l-4 l-5 2-l 2-3 e-4 2-7 2-8 2-12 4 iii Figures c Figure 2-7 Figure 2-8 Figure 2-9 Figure 2-10 Figure Figure Figure Figure Figure Figure Figure Figure Figure 2-11 2-12 2-13 2-14 2-15 Figure 3-l Figure 3-2 2-16 2-17 2-18 2-19 Page Typical direct design chart for As in horizontal bending. Steel layouts at closed horizontal sections of riser. Suggested tabular form for design of closed sections for horizontal bending. Layout of horizontal steel in sections at the conduit entrance. Vertical section through sidewall. Vertical section through endwall. Sketches for analysis of pinned frame. Pinned frame deflections. Vertical steel at wall-to-footing connection. Typical load division curve. Assumed embankment loading. Analysis of bearing pressures. Moment in footing due to vertical bending. Direct design D = 30 in. Plan of trial chart for horizontal 2-12 2-15 2-16 2-17 2-18 2-22 2-23 2-25 2-27 2-28 2-29 2-30 2-32 bending, footing. 3-4 3-9 Tables Table Table Table Table Table Table Table Table Table 2-l 2-2 2-3 2-4 2-5 2-6 2-7 2-8 2-9 Table 3-l Table 3-2 Cover slab design summary. Cover slab and cover slab wall steel. Force coefficients for horizontal bending, n. Moment coefficients assuming prismatic members, and using the PCA moment concentrated reactions, corrections - not to be used for design. Data for analyses with non-prismatic members. Moment coefficients for horizontal bending,, m. Data for preparation of direct design charts for horizontal bending. Values of functions. Pinned frame corner moments and deflection coefficients. Summary of riser wall design for horizontal bending. Vertical steel for moment from embankment loading at usual closed sections. 2-2 2-3 2-5 2-8 2-9 2-10 2-13 2-21 2-24 3-5 3-7 V A i: A, a 3 * ab a, B b C C D d d" E e F fc fps f, H equivalent area of reinforcing = area of footing; steel = area of reinforcing = ratio used to obtain properties of non-prismatic of flow = area of the conduit = = = = = = area of the riser "weighted" width of riser endwall width of reinforced concrete member carry-over factor distance from center of gravity axis to extreme pipe conduit = effective force compressive members; area fiber diameter depth of reinforced =d -t/2 = modulus of elasticity = base of Naperisn logarithms = = = = = steel stress concrete = 2.7183 member - - - in concrete foot per second tensile stress in reinforcing steel Hh hs head = head over crest of the cove-ed inlet of the riser = depth of embanlunent or sediment at the riser at the section below the crest of the covered inlet hvr hw h, I j = = = = = hx velocity head in the riser inward pressure on riser wsll in feet of water distance from crest of covered inlet to point under consideration second moment of area, moment of inertia ratio used in reinforced concrete relations soil pressure to vertical soil pressure K = ratio of lateral deflection coefficient KY = horizontal k = kip, thousand pounds; stiffness coefficient klf = kips per lineal foot Revised 8-l-68 vi c: ksf ksi L M MF = kips per square foot = kips per square inch = length; span length, C.C. of supports = moment = fixed end moment moment MS = equivalent moment in the riser wall at the wall-to-footing connection Mvo = vertical moment in the riser wall at section under consideration Mvx= vertical In = moment coefficient NE = direct compressive force in the riser endwall forces, but not including uplift NGR = sum of vertical distance from pipe invert at the riser to crest of the covered Nib = vertical inlet of the riser distance from pipe invert at the riser to soil surface. N\T~~= vertical The soil surface may be either the sediment or the embankment (berm) surface. No = direct vertical compressive force at the wall-to-footing connection Ns = direct compressive force in the riser sidewall distance from the soil surface to the crest of the covered Nsh = vertical inlet of the riser n = modular ratio; force coefficient pressure per unit area P = soil bearing pressure; pcf = pounds per cubic foot psf = pounds per square foot psi = pounds per square inch and shrinkage steel ratio in reinforced concrete pt = temperature = unit load; uniformly distributed load q qKx = the unit load resisted by horizontal bending at the section under consideration qvx = the unit load resisted by vertical bending at the section under consideration qX = the total unit load at the section under consideration R = redundant force spacing of reinforcing steel S = stiffness; T&S = temperature and shrinkage riser wall thickness t = thickness; = footing thickness tf = bond stress in concrete U v = total shear; volume 4 vii VVQ = shear in the riser wall at the wall-to-footing connection due to vertical bending V, = shear in the riser wall at the section under consideration due to vertical bending = shear stress V in concrete; velocity of flow of flow in the conduit vb = mean velocity of flow in the riser vr = mean velocity in the direction of M; weight W = width of footing = unit weight, unit weight of water W wb = buoyant unit weight of soil wm = moist unit weight of soil unit weight of soil WS = saturated X = distance from the wall-to-footing connection to the section under consideration deflection of the riser wall at the section under Y = horizontal consideration B = (j+jw4 h = distribution Co = perimeter factor of reinforcing steel l-1 TECRRX!ALRELEASE NUMBER 30 STRUCTURAL DESIGN OF STANDARDCOVEREDRISERS h CHAPTER 1. CRITERIA Proportions, Details, , Standard and Data Refer to Engineering Standard Drawing ES-150, "Drop Inlet Spillways, Standard for Covered Top Riser", and to Technical Release No. 29 "Hydraulics of Two-way Covered Risers". Structural detail drawings shall conform with practice as shown in the latest edition of "Manual of Standard Practice for Detailing Reinforced Concrete Structures" by AC1 Committee 315. Limitations on the Use of the Standard Plans Riser Heights For the purpose of developing and presenting the standard risers, the following vertical distances are defined: N-zh = vertical distance from pipe invert at the riser to crest of the covered inlet of the riser distance from pipe invert at the riser to Nis = vertical soil surface. The soil surface may be either the sediment or the embankment (berm) surface. Nsh = vertical distance from the soil surface to the crest of the covered inlet of the riser. The standard risers shall be designed using 5 ft increments and combinations of Nib and Nis. N,h shall not exceed 20 ft, Nis shall not exceed 35 ft, and Nib shall not exceed 40 ft nor be less than 3D. Pipe Velocities The maximum allowable mean velocity in the pipe conduit of standard risers is vb( -) must exceed 30 fps at an = 30 fPs= If the velocity actual site, the riser to be used, particularly the elbow section, should be treated as a special design. Ice Conditions Ice pressures are highly indeterminate, therefore the standard risers shall not be designed for ice loads. Where ice of considerable thickness can occur, the riser should be located in the embankment at a berm, thus eliminating ice pressures. 1-2 Allowable Stresses and Bearing Pressures Concrete Class 4000 concrete shall be assumed in the design of the standard risers. Allowable concrete stresses and other criteria shall be in accordance with National Engineering Handbook, Section 6, sub-section 4., Reinforced Concrete (g-64 revision) except as modified in the following notes: constant allowable bond stresses (1) As a design convenience, shall be used for all bar sizes 5 #7, these are: tension top bars, u = 245 psi all other tension bars, u = 350 psi (2) Shear stress, as a measure of diagonal tension, shall be limited so that web steel is not required. (3) Minimum thickness of cover slab is 8 in. (4) Minimum thickness of riser walls is 10 in. (5) Wall thickness increments shall not exceed 3 in. Reinforcing Steel Intermediate grade steel sh&Ll be assumed in the design of the standard risers. Allowable steel stresses and other criteria shall be in accordConcrete (g-64 revision) exance with JTEH-6, sub-section 4., Reinforced cept that the minimum steel ratio for principal steel and for temperature and shrinkage steel shall be pt = 0.002 in each face in each direction, thicknesses greater than 16 inches shall be considered as 16 inches. Earth Rearing Pressures The allowable bearing values given are the allowable excess pressures over the pressure whfch would exist at the elevation of the bottom of the footing if the riser were not present. (1) Saturated foundation: Allowable average excess pressure =l,OOO psf Allowable maximum excess pressure = 2,000 psf (2) Moist foundation Twice the above values. In no case shall the line of action of the reaction lie without the middle The loading conditions to be investigated are listed third of the base. under "Stability Analyses". Loads Loads on Riser Walls The design of horizontal sider both lateral soil and vertical sections of riser walls pressure and water pressure loadings. must con- Lateral soil pressures. - For the design of the riser walls, lateral soil pressures shall be assumed uniformly distributed around the riser and Kq = 45 pcf where K = the ratio of lateral to vertical soil pressures and wb = buoyant unit weight of soil. l-3 Water pressures during pipe flow. - The loading on the riser wall during pipe flow is equal to the difference between the pressures on the exterior and interior sides of the wall as illustrated in Figure l-l. Hh . . Figure l-l. Tests on risers difference inlet l . Ap/w = (Hh + h,) - (p/w) Water pressures of the standard may be taken as of the riser * h-r to a distance on riser walls proportions show that = 6.0 from the crest difference For vb(mm) vr = 30 fPs: = (ab/+)y, = 3013.82 hvr = (vr>2/2g = ($/3D2hb = q/3-82 = 7.85 fps = (7.85)2/2g = 0.96 ft Thus, 4/w = 6.0 x 0.96 = 5.76 ft and 4/w = 3.0 x 0.96 = 2.88 ft where vr = mean velocity of flow ar = area of the riser ab = area of the conduit pipe in the riser flow. the pressure of the covered equal to 1.5D below the crest is !?iiihL h - 3.0 below distance v-r where hvr is the velocity head in the riser. pressure during and the 1.5D below the crest, l-4 For design, use &/w = 6.0 ft and 3.0 ft respectively. Figure 1-2 illustrates a method of representing the various heads involNote that negative pressures (below atmospheric) ved during pipe flow. The maximum possible are possible at and near the crest of the riser. magnitude of these negative pressures is about: = 300 psf for D = 24 in. (6 hvr - 0.5~)62.4 negative head hx I; Ap/w lp/w=inside I(" + hx) = outside Figure l-2. D/2 - heat heat Representation of heads during pipe flow. Composite wall pressure diagram for design. - For design purposes, two loading conditions are defined: (1) pipe flow - pressures as described above, no flow - water surface at the crest of the covered (2) inlet of the riser, lower inlets, if any, assumed plugged. These two conditions may be combined and a composite diagram drawn as The resulting diagram will contain, when illustrated in Figure l-3. N,h > 6, three straight lines given by: for 0 5 h, I 6.0 (1) h, = 6.0 for 6.0 5 h, S Nsh (2) $,, = hx for N,h 5 hx s Nib (3) h, = hx + 0.72 h, l-5 6' w, / / / t 1 \ hX Nsh 7 A hS 0 . .A Kwbhs 9 Figure ”A hx l-3. embanlanent or ' sediment level v Composite wall pressure diagram for risers (vb(ma) = 30 fps). design of standard where h, = inward pressure on riser wall .n feet of water h, = distance from crest of covered inlet to point under consideration h, = depth of embankment or sediment at the riser to the section h, below the crest of the covered inlet N,h and Nib as previously defined. Note that the crest KWb/W = 4/w = 6.0 ft has been used to a distance of 6.0 ft below of the covered inlet, and that 0.72 is obtained from 45/62.4 = 0.72. Loads on Cover Slab The cover slab live load shall be 100 psf. The weight of any equipment to be installed on the cover slab shall be incorporated in a special design. Bnbankment Load on Riser For stability analyses and to check the vertical steel required in the downstream endwall, it shall be assumed, for risers located in the embankment, that the difference between the downstream and the upstream lateral earth pressures is Kwm = 50 pcf on the downstream endwall for 1-6 moist conditions and is Kn = 30 pcf for saturated conditions. A triangular pressure distribution shall be used, but the resultant force shall be assumed to act at mid-height instead of at third-height of h, to account for possible "arching effect". Take the unit soil 140 PCf. Wm = Ws = weights for moist or saturated conditions as Neglect friction which may act on the side-walls. Wind Risers located in the reservoir area shall be designed for wind acting over the entire sidewall using 50 pounds per square foot pressure. Risers located in the embankment shsll not be designed for wind. However, the catalog of available standard risers, when prepared, will specify a maximum allowable wind projection. This wind projection is the vertical distance between the surface of the backfill and the top of the riser at any stage of construction. Flotation (1) (2) Criteria When the riser is located in the reservoir area, the ratio of the weight of the riser to the weight of the volume of water displaced by the riser shall not be less than 1.5. Low stage inlet(s), if any, shall be assumed plugged for this computation. When the riser is located in the embankment - same as (l), but add to the weight of the riser, the buoyant weight of the submerged fill over the riser footing projections. Take the buoyant unit weight as w-b = 50 pcf. Location of Construction Joints in the Riser Walls The first construction joint above the top of the footing shall be D + 12 inches above the pipe invert at the conduit entrance0 The distance between the first and second, and all other pairs of construction joints below the topmost joint in the riser walls shall be 5 ft except that the distance between the topmost and the next to the topmost joint shall be 4 ft for risers having D = 36 in. The topmost construction joint in the riser walls shall be 7.0, 6.5, 7.0, 10.5, and lo,0 ft below the crest of the covered inlet of the riser for risers having D = 24, 30, 36, 42, and 48 in. respectively. The distance between the first and second construction joints above the The blank top of the footing shall be left blank on the standard plans. distance makes it possible to adapt the plans for a specific standard This adaptability of the standard plans riser to a range of heights. imposes that there can not be a change in wall thickness at the second construction joint. 2-1 cHAFTER2. METHODSOF ANALYSIS AND DESIGN PF0XDUFU3S Cover Slab Walls b i . The cover slab wslls support the cover slab, of the cantilever beams. In the top portion will be 10 in. thick (the minimum thickness). the cover slab walls placement difficulties, With 10 in. walls, #5 @ 15" C.C. are thick. give 0.25 Pt = 120 = 0.0021 2 0.002. With this show that wall thickness and amount of steel, further analysis is unnecessary. acting as variable depth riser, the riser walls Thus, to avoid steel will also be made 10 in. required in each face to rough computations will Cover Slab The minimum thiclmess of the cover slab is 8 in., this is an adequate The total loading is 200 psf (100 psf live thickness for all D values. Cover slab span is 3D + 10 in. C.C. of supports with + 100 psf dead). Thus, the cover slab need be designed only once for each 10 in. walls. (The only exception to this might occur in the case of conduit size D. short risers which require additional wall thickness to satisfy the floin which event the procedures given below can be suittation criteria ably modified.) Moments in the cover slab are highly indeterminate. Therefore, the positive center moments shall be conservatively taken as l/8 qL2. Negative steel in the amounts required moments shall not be computed, but negative for T & S (temperature and shrinkage) shall be provided and shall be lapped with the outside T & S cover slab wall steel. A construction joint shall be provided in the cover slab walls at the elevation of the high stage crest. q = 200 psf Figure 2-l. Definition (live + dead) sketch of cover slab. 2-2 The cover slab design follows from a consideration of Figure d = 8 - 2.5 = 5.5 in. As(min) = 0.002 x 8 x 12 = 0.192 sq in./ft #4 @ 12 = 0.20 sq in./ft #5 @ 15 = 0.25 sq in./ft v max = 1.50 qD = 1.50 vmsx = CO Tnax 25D = - ujd = 350 x 718 x 5.5 = D/67.3 in./ft Vmm = - qd bd l/8 = X 200 X D/l2 As may be determined Table = 25D ibS/ft 25~ - 200(5.5/u)= 12 x 5.5 x 0.200( 3D ,'F)' directly 2-l. Cover o . 37gD - 1.4 psi = O.O001735(3D from ~~-164, slab design 30 36 vmax, Psi 7 10 0.36 42 48 12 14 17 0.45 0.54 0.62 0.71 1.2 l-7 2.4 3.2 4.1 0.19 0.20 0.29 0.39 0.50 #[email protected] #[email protected] #[email protected] #4z # %7 l/2- --- M, ft kips/ft -A, req'd., sq in./ft Steel selected kips/ft summary, 24 in./ft + 1O)2 ft sheet 1 of 3. D, inches co req'd., 2-1: --II- -- The cover slab layout is shown in Figure 2-2 and the cover steel selected is tabulated in Table 2-2. The layout must be modified locally near the 30 in. diameter manhole in the cover slab. 2-3 Table 2-2. Cover slab and cover slab wall steel. 1 CWl, cw2, cw3, cw4 = #pa5 rD cs5 24 30 #[email protected] #[email protected] 42 36 -#[email protected] cs6 = 48 #[email protected] #%7 l/2 #me5 cs7, cs8 = #[email protected] - cs6 cw4 Cw2--\ \ e---cw1 AeH -construction 2" Clear Figure 2-2. I joint cw3/ Cover Cover slab and cover Riser Walls, Horizontal slab wall steel lavout. Bending Sections For overall economy the sidewalls and endwalls shall have the same thickness at any horizontal section. Since equal thicknesses are used, moments and direct compressive forces can be expressed conveniently as functions of t/D. Figure 2-3 shows the various moments and forces of interest. Closed Equilibrium ---- relations. - The relations be written directly from a consideration NE = l/2 q(3D + 2t) NE/qD Ns = l/2 q(D + 2t) Ns;~~ NK = O.~O~(NE + MS) NK/~D = 1.414 q(D I- t) for the compressive of statics as: = l/2 (3 + 2t/D) = l/2 (1 + 2t/D) = 1.414 (1 + t/D) forces can 2-4 3D + t I: I I: I 31, I I tttttt 9 SF NE L I NK = resultant of components of NE and NS which are perpendicular to the cut section. Figure 2-3. Definition sketch for horizontal bending. ‘/ 2-5 These relations of the endwall Table 2-3. together with the shear in the sidewall are swnmar ized in Table 2-3. Force coefficients for horizontal bending, t/D 0.00 0.25 0.50 0.75 1.00 Ns 0.50 1.50 1.41 1.50 0.75 1.75 1.77 1.50 1.00 2.00 2.12 1.25 2.25 2.48 1.50 1.50 NE NK VSF 1.50 at the face n. 2.50 2.83 1.50 Ni or Vi = niqD The relations for the various moments can also be written from a consideration of statics, however MK must be known before the relations can be evaluated. The relations are: Msc = i s(3D + ‘d2 - MK MSF= 6 q(3Jd2 - %c MEC =EpC-$q(D+tj2 Mm = Mx + i q(Dj2 Msc 3 = !j (3 + t/Dj2 -s qD MSF = 1.125 - %C - sD2 sD2 %C -=-- MK i( 1 + qD2 qD2 MEF = [email protected]+ 0.125 qD2 t/Dj2 qD2 Note that the expressions for MsC and MEC assume, in common with most structural analyses, the support reactions for any member are concentrated at the support centerlines. Analysis for corner moments, MK. - Thought should be given to the effects of the assumptions used in analyzing for moments. Any reasonable method of analysis may be employed (as Moment Distribution, Slope Deflection, etc.) but the results may vary widely depending on Conjugate Structure, the assumptions followed. The effects of using two basically different assumptions are presented below. Moment Distribution is used as the method of analysis because of its simplicity due to symmetry of both loading and shape. Members are prismatic. - - The basic assumption is: the members of the closed frame are prismatic. Under this assumption, one cycle of Moment Distribution results in final values for MK, since together with symmetry of loading and shape, the sidewall and endwall carry-over factors 2-6 are equal. where Thus MK is given by: MF = fixed end moment, and h = distribution factor. In the above equations, justed. The distribution S = stiffness substitute factors = YU magnitudes only, signs are determined from: or ad- t so ss a 3D1+ t are already and SE a: -D+t1 and kE = thus xs The fixed = SS $3 + SE end moments may be written SE sS + sE as: q(3D + t>2 and &$ = $ q(D + t)2 Note that these expressions, along with those for support reactions are concentrated at the support XSC and MEC, assume the centerlines. Observe that even if the assumption of prismatic members was correct, values for moments obtained from the above analysis would be incorrect. The moment values would be incorrect because beam reactions are not concentrated at support centerlines. The reactions are in reality distributed in some unknown way over the thickness of the member providing the support. If the reaction (and hence shear) distribution were known, it would be possible to compute correct values for MF from which correct values of MK could be obtained. Similarly with the shear distribution known, correct expressions for MsC and Mx could be written. Since the approximate procedure is shear distribution is not known, the following sometimes advocated to obtain better values of moments. Figure 2-4 shows the shear distribution assumed by usual theory. moment at the face of the support using usual theory would be: MF = MK - k&l where &4 = VA(t/2). The Portland Cement Association in its "Continuity in Concrete Frames" (page 28), would give the moment at the face as: where NPCA = VA(t/T). MF = N - &=A The Building 2-7 The difference 6&d in AM values = V&/2) is: - v&/3) Thus, the FCA moment correction = VA(+) is VA(t/6). c Figure Or, for 2-4. Shear distribution theory. the sidewalls: S(EM)g/qD2 And, for assumed by usual = &(s + &) - &($ + &) endwalls: 6(nM)&D2 The procedure using these moment corrections would then be: (1) compute using the assumptions of prismatic members and concentrated 53, etc. (2) add these moment corrections to negative moments and subreactions, tract them from positive moments. Many engineers, however, would not reduce the positive moments. Table 2-4 gives the moment coefficients obtained by use of the above procedure. These values are given for purposes of comparison only, they shall not be used in the design of standard covered risers. 2-a Table 2-4. Moment coefficients assuming prismatic members, concentrated reactions, and using the FCA moment corrections - not to be used for design. 0 0.00 0.25 0.50 0.75 1.00 MK 0.58 0.58 0.54 0.58 0.46 0.67 0.54 0.77 0.50 0.62 0.66 0.88 1.00 0.45 0.67 0.41 0.71 0.71 0.54 0.59 0.75 0.63 are for M/qD2 MSF NYC M?3F ME 0.58 0.62 0.50 Moment coefficients How well the PCA moment correction takes assumption of concentrated reactions is error due to the assumption of prismatic ratio of t/D. Since high ratios of t/D is desirable that a more nearly correct care of the error due to the not known. In any case, the members increases with the will occur in some risers, it analysis be employed. Members are non-prismatic. - - The basic assumption is: the members of the closed frame are non-prismatic and have moments of inertia which approach infinity outside of the clear span limits. Figure 2-5 shows this variation in moment of inertia. The assumption of large values of moments of inertia outside of the clear span limits not only avoids the error due to the previous assumption of prismatic members, but it also reduces the error due to the assumption of concentrated reactions. The error due to the assumption of concentrated reactions is reduced because moments in regions of large moments of inertia have little influence on final moments in indeterminate structures, that is, M/I values Therefore the FCA moment corrections in such regions approach zero. should not be applied to the moments resulting from this analysis. Figure 2-5. Assumed variation in moment of inertia. 2-9 Because the members are non-prismatic, the sidewall and endwall carry-over factors are not equal. Hence, the distribution of moments has to be performed. The required data is obtained as follows: aSLS = t/2 a& = t/2 &E 1 = 2 qE+2 or +- as and qE+2 thus C!i = carry-over factor Si = stiffness MT = fixed = k$ i Ccki Li end moment = m;qLT where C!i = a function of ai where ki = a function of ai where ml? 2 = a function of ai Table 2-5 gives values of C, k, andm? It is obtained page 23 of "Handbook of Frame Constants", by the FCA. Table 2-Y. Data for Carry-over Factors a 0.00 0.05 0.10 0.15 0.20 0.25 Again analysis with members. SS As = SS i SE Stiffness Coefficient C k 0.500 0.575 0.648 0.719 0.786 0.846 4.00 5.23 7.11 10.17 15.56 26.00 and hE= in part from non-prismatic Fixed end Co~f~~~~ent mF 0.0833 0.0913 0.0983 0.1046 0.1100 0.~46 SFI SS + SE Table 2-6 gives the moment coefficients obtained by use of the above procedure. These values shall be used in the design of standard covered risers. 2-10 Table 2-6. Moment coefficients bending, m. for horizontal t/D 0.00 o.-25 0.50 MK MSF Msc &a? MEC 0.58 0.58 0.75 0.55 0.94 1.15 0.51 0.54 0.58 0.46 0.57 0.68 0.56 o-53 0.59 0.78 0.66 0.61 0.89 0.77 1.38 0.50 0.62 1.00 0.88 Mi = mtqD2 Design approach. - The process of design of closed sections of riser walls for horizontal bending can be reduced to a procedure which may be both quickly and accurately performed. Considerations. - - Using equal thicknesses for sidewalls and endwalls, the minimum thickness is governed by shear stress (as a measure of diagonal tension) in the sidewalls [d] distance from the face of the endSince thickness is governed by shear, sections will be underwalls. stressed in compression. Hence, T & S steel in the compression side of a section will not be counted upon as compressive steel, that is, the presence or absence of compressive steel has a negligible effect on the amount of tensile steel required in such a section. The critical section for bond is in the sidewalls at the face of the endwall. Computations, using the coefficients for MsC to locate the show that the ratio of required point of inflection in the sidewalls, perimeter of the f+> kside steel to the required perimeter of the (-1 outside steel is: JET* VSF - 1.50 1.50 - 0.38 = 0.745 for t/D 5 1.00 where VP1 is the shear at the point of inflection. Comparisons of the coefficients for MsF and MsC for a given show (since NS is the same for both moments): t/D value AsSF ' AsSC for t/D 2 0.17 (min. t/D = j$ = 0.208) Computations for AsEF using Mm and NE, and computations for ing MsC and NS will show, for given values of hw, t, and D: h, 2 ksc for all t/D values, however do not differ significantly. The corner, with MK and NK., is not critical given the usual standard bend. the required if the negative Assc us- steel areas steel is 2-11 consideraDirect design by charts. - - In the light of the preceding it is possible to construct charts which will permit the dirtions, ect selection of wall thicluless, steel areas, and steel perimeters for given wall loadings and conduit diameter. t and Co vs. hw for f given , x_ D: Determine (hw),,, for VSF - qt d/12) v= bd given t, which makes v = 70 psi = s+1.5D - &, = 62.4(hw)vo (9 - +12b . I rearranging . (b)-m and substituting values, = L5D1314; 0833 ft t - 2.5 Determine (Co),, required (@SF) when v = 70 psi ujd = vbd + q(d/12) VSF = b’), l or (co)~o = substituting vb + (q/12) uj values, (co)vo = 3.918 + 0.02426(hw)70 in./ft, for where D is in ft, t is in inches, h, is in ft bar sizes 5 #7 Thus curves similar to Figure 2-6 can be drawn for each conduit diato hw for a given t and D. meter, since CO and v are proportional t and As vs. hw for given D: The relation of As vs. hw for a given t and D is nearly linear since sections are under-reinforced. Hence, only the As required (@EF) for the corresponding values of t and b making v = 70 psi need be computed. These A, values may be computed from MEF and NE using ~~-164, sheet 1 of 3. Thus curves similar to Figure 2-7 can be drawn for Table 2-7 provides all the data necessary to charts for each of the standard pipe conduit shows the steel layout at closed horizontal Using the direct design charts the steel is RHL less HH2 for All each conduit prepare the diameters. sections of selected as by As but not less than 75 percent Co, and not than that required for T & S. by A, and co, and not less than that required T 8~ S. other by As for T & S. diameter. direct design Figure 2-8 the risers. follows: 2-12 Figure Typical 2-6. direct design For a given /-A,/ 0 u\rurrr, min\ for chart for CO in horizontal bending. D Pt(min) = 0*002 *. \\ . \'\ \' \ L '\ \ \ \ \ \ \ \ t, > t, > t, I 0 Figure 2-7. Allowable shear is exceeded to right of this line 1 Ty-pical direct design chart for As in horizontal bending. 2-15 Typical Layout (not to scale) Detail at Cover Slab Walls CW2 Figure 2-8. Steel layouts at closed horizontal sections Wall thickness and steel selection. - Use of a tabular that shown in Figure 2-9 will facilitate design. of riser. form similar to Observe that for a given value of loading on the riser (hw) at the four items must be determined: wall thicksection under consideration, The last three items ness (t), (+> steel, (-> steel, and T & S steel. Hence, trial solutions using depend on the wall thickness selected. different thicknesses should be investigated. The combination finally chosen should reflect consideration of the requirements of adjacent sections to insure that the whole will fit together. Sections at Low Stage Inlets No low stage inlet will be shown on the standards. The location and size of this opening (if any) and the necessary steel changes are to be handled by the field as a modification of the standard plans. It should be recognized that such openings, if sufficiently large, will cause a significant change in structural behavior from that of the usual closed section. Sections at the Conduit Entrance An exact analysis of horizontal steel requirements in this region the riser walls is complicated by two main factors: (1) horizontal structural behavior varies between the limits of usual closed section behavior and pinned ended frame behavior, and the connection of the riser walls to the footing (2) causes vertical bending and tends to restrain horizontal bending (this effect is presented under "wall-to-footing connection"), hence the load on the walls at any distance above the footing is divided between that producing horizontal bending and that producing vertical bending. of hX Range value for h, range) (+)%eel t h, CM=- !4in. r Trial A, ft 1 (of Zter) 2 r:selected Required t 75fJo in. in. in.2/ft in./ft 3 4 5 6 V Colon 3 obtained from riser design Columns 5 and 8, 9, and 11 obtained column 6 I- 75% of column 9. Figure 2-g. . ..m . ., ,,. . . I yps A, 7 CO in. yft in./ft 8 9 Selected #@S #@S 10 Use in.2/ft 11 A chart for given &. from r .ser design chart Suggested tabular (-)?Eeel Required - m, m-l, m2 T and S Steel Required Selected form for design for given of closed hw and t. sections for horizontal bending. .m . . . . . . . .. . . ,----,-,“-,-;-“_111 -x--_. ^ m . . . 2-17 show that the following procedure Analyses, presented subsequently, yields conservative results for required amounts of horizontal steel: (1) At and above D distance above the pipe invert at the conduit entrance - design for usual closed section behavior under the assumption that the entire load is resisted by horizontal bending. (2) Between D distance above the pipe invert and the - hold the steel amounts contop of the footing stant at the values determined for D distance above the pipe invert. The layout of horizontal steel can therefore be the same as for the usual closed sections except for the omission of two RR2 bars and the addition of two RH4 bars as shown in Figure 2-10. RH4 Figure 2-10. Layout of horizontal steel entrance. in sections at the conduit 2-18 Riser Wall-to-Footing Walls, Vertical Rending Connection Rending is produced in a vertical direction in the riser walls wherever a discontinuity of section occurs. Ususlly the action is not serious and is adequately resisted by the usual vertical steel provided for T & S. However, vertical bending of the same order of magnitude as is present in horizontal bending is produced by the wall-to-footing connection, since the riser walls cannot deflect horizontally at this location. When considering riser wall design, the wall-to-footing connection is assumed to be located at the elevation of the pipe invert at the conduit entrance and the variation in wall section due to the round bottom is neglected. Vertical flexure in sidewalls. - No vertical bending would occur at the w&L-to-footing connection if the riser walls were not connected to the footing, that is, if the walls merely rested on the footing without However, with rotation and translation prevented, moments friction. and shears are produced to satisfy the requirements of geometry. Figure 2-11 illustrates the various deflected shapes and the loading on the wall. sidewsJ-1 deflection no-load position of sidewall sidewall deflection if I wall not connected to I footing -v / Figure 2-11. Vertical section elevation of wall-to-footing connection through sidewall +Y Let: moment in the riser wall at the wall-to-footing Mvo = vertical connection shear in the riser wall at the wall-to-footing connection due to vertical bending unit load at the section under consideration sx = the total vvo= sm Y the unit load resisted under consideration the unit load resisted under consideration deflection = horizontal under consideration. = by horizontal by vertical of the riser bending bending wsll at the section at the section at the section 2-19 l Then at any section: qX = sm + SlJx But the horizontal deflection the minus sign at any section is used since may be expressed as: (Y) is in the minus direction. Here: Es' = athehorizontal location deflection coefficient of the section under sv-x = s, -qHx=qx+=-Y The differential equation EI ax" d4Y = zx which depends on consideration. R-r KyD4 of the elastic curve of a beam is: where ZX is a load function. Here: zx = - qiy( or I+-qx-- ;4 y and letting 484 = -&$ Y then It is possible to solve this equation by writing the and evaluating the four constants of integration by conditions. However, the equation d4Y + 48% = 0 dx4 has already been solved for a semi-infinite beam on Part II, page 12, tion (see "Strength of Materials", loaded with MVO and VVo at its ends acting with the general solution using the boundary an elastic foundaby yimoshenko), senses shown. 2-20 Timoshenko's complimentary solution: cm w - /3MVo(cosBX - [email protected])] together '= lead with the particular solution: a- qx @%I to the following expressions: %o = 0.1074 Vvo = $1 - %x= -- VVO e-BXsinBX B + &JO e-Bx([email protected] Vvx= - Vvoe+x(eos13X - sinBX) 2qB > and + sinBX) [email protected]+xsingX where MVX = vertical moment in the riser wall at section under consideration vm = shear in the riser wall at the section under consideration due to vertical bending = the total unit load at the wall-to-footing connection 9 (9x)X& ' These equations follow the usual M The units sign convention: V of the various quantities are: MVO, MVX = ft kips/ft vvo9 Q-X = kips/ft Q B q 1 Emensionless = ft-l = k!f/ft Revised 8-l-6 2-21 The values of various functions are given for convenience in Table 2-8. Moments "damp out" quickly with distance from the wall-to-footing connection. This may be seen by examination of the expression for R!vx" Hence, the usual amounts of T & S steel soon become adequate to resist the vertical bending. i Table 2-8. e+'sin PX 0.0 SX e-SX(cosSX 0.000 0.291 0.5 1.000 0.242 0.014 - 0.011 - 0.013 1.5 2.0 - 0.011 - 0.006 - - sinSX) 1.000 - 0.310 0.223 0.123 0.049 0.007 e+'([email protected] + sinSX) 0.823 0.508 0.238 0.067 - 0.017 - 0.042 - 0.039 - 0.026 1.0 2.5 3.0 3.5 4.0 4.5 5.0 Values of functions. - 0.111 - 0.207 - 0.179 - 0.115 - 0.056 - 0.018 0.002 0.008 0.008 0.005 to that of the Verticsl flexure in endwalls. - This case is similar sidewalls, except that endwall deflections oppose the direction of Also, intuitively, loading a~&- hence, various signs are reversed. vertical bending in the endwslls is small relative to that in the sidewaLLs. Thus, T & S steel, properly anchored, msy be adequate. Figure 2-12 illustrates the various deflected shapes and the loading on the wall. The relations again are: vvo =; (1 - L&L!$ h=+Be "O -BXsinSX but Vm = + Vvo e-BX(cospx These quantities - Mvo e*'(cosBX + [email protected]) - SinBX) + 24&3 are as defined for sidewalls. e-f3XsinSX 2-22 Compare with Figure 2-11 for sidewalls. Figure Evaluation 2-12. Vertical section through of coefficients endwall. Icy. - Before the vertical. the horizontal deflection and shears can be evaluated, Ky must be determined. flexure moments coefficients structural behavior of the riser As previously noted, the horizontal walls, at and near the conduit entrance, is intermediate between that of the usual closed section and that of a pinned ended frame. Vertical flexure increases with horizontal deflections, thus conservative design dictates that KY be evaluated on the basis of pinned frame action since a pinned frame has larger deflections than a similar but closed frame. Also, the values obtained for corner moments regarding variations ced by the assumptions, Conservatism is in analyzing the structure. tions giving small corner moments and hence, (MK) are directly influenin moments of inertia, used again served by using assumplarge sidewall deflections. Therefore, KY, is evaluated on the basis of pinned frame action and prismatic members. Figure 2-13 shows the moment diagrams resulting from the statical system selected. Using (R) as the redundant force 2-23 and taking moments of moment areas abouti a line through in accordance with the Conjugate Structure concept: z(3D + tj2 + $3D 2 3 --X =2x x (3D +t> + tj2 x 2 x (3D +t> x (D + t) x (3D + t) 3( D +t12 $X the supports x (D +t) x (3D +t) R(3D + t> x (3D +t> + R(3D + t> x (D +t) x $ x (3D + t) x (3D + t) - - = original II structure II s(D+t)2 p+t )2 v )2R(3D+t, r\ ( > \ 0 Figure ’ Z-13. Sketches for 7I c > + R(3D+t > analysis = final of pinned frame. moments 2-24 Thus: R(3D + t)(36 + 20%/D) = qD2[3(3 + t/D)' + 6(3 + t/D)*(l - (1 +t/D)3] + t/D) and, by statics MK = $3D From Figure I- t)2 - R(3D + t) 2-14, the mid-span For sidewall Y = m' For endwall Y = i g Solutions of the equations given in Table 2-9, where dEI - $ 'g (3 + t/D)4 (1 + t/D)* for may be written deflections R, !I(, - & (3 + t/D)* g and Y yield as: (1 i- t/D)4 values for KY as Ky==Y qD4 Table Pinned frame corner coefficients. 2-9. t/D morhents and deflection 0.00 0.25 0.50 0.75 1.00 Sidewall KY 0.616 0.872 1.188 1.573 2.043 Endwall KY 0.085 0.140 0.215 0.314 o-437 0.78 0.88 1.00 1.14 1.29 MK sr)' Revised u-65 2-25 l I PI . endwall deflections sidewall Figure 2-14. deflections Finned frame deflections. 2-26 Example of computation of MvO and VVo. - The following example is presented for two purposes; first, to indicate the ease with which the computations may be made and second, to indicate the order of magnitude of vertical bending. Assume: D = 4.0 ft t =24in. hw = 60 ft at the wall-to-footing connection . l . q = 3.74 klf/ft At center of sidewall: t/D . = 0.50 l . KY = 1.188 B4 = 4 x 1.1;8 P2 B =& %O vvo At center = 24148 x (4)4 = & = 0.16g/ft = 3.74 x 34.9 2 = 3.4 0.1 -Is 9 (I- (1 _ 3.7~'~"~~16g) 2 x 3*74 0.1074x o.l6g) = 54.1 ft = 20.3 kips/ft w?s/ft of endwall: = 0.50 t/D . l . KY = 0.2l5 B = 0.259 = 24.7 ft kips/ft vvo =&$'l- 2 x ~:~~7~ o.2~)= 13.6 kips/f't Revised u-65 2-27 l Wall thickness by shear due to vertical bending. - The wall thickness required by shear at [a] distance above the wall-to-footing connection at the center of the sidewalls due to vertical action may be greater than the thickness required by shear at D distance above the connection action. This may be checked by: due to horizontal . T . h&d bd v= C S 70 psi where d =t - 3.5 at the center of Vertical steel. - Determine the outside steel required The force system consists of the moment MvC and a direct the sidewall. If the amount of steel thus force NC due to the weight of the riser. required exceeds that required for T 8~ S, the height at which T & S steel is adequate will have to be checked. Thus, throughout the length of the sidewall, for the inside steel use that required by T & S, for the outside steel use the larger of that required for T & S or that required for vertical bending at the center of the sidewall. In the endwall follow a procedure similar to that for the sidewalls except note that vertical bending produces tension in the inside steel. it will also be ade(Note, if T & S steel is adequate in the sidewalls quate in the endwall.) Figure P-15 illustrates the steel concerned. 5" to Center of Steel Figure Z-15. Vertical steel at wall-to-footing connection. division of wall loading Division of wsll loading. - The theoretical between horizontal and vertical bending along a vertical line may be obtained as follows. From the sidewall investigation (the ssme end result is obtained from the endwall investigation): 2-28 substitution gives of the expressions for Y, VVO, and MvO and simplifying : ¶.m = sx - q[e-BX(COSf3X + [email protected]) - y e+'sinSX] Thus qHX varies from qHx = 0 at the wall-to-footing connection to qm = qX at some distance above the connection as shown by Figure 2-16. This distance may be determined by setting the term in brackets in the above equation to zero and solving for X. The procedure for determining the required horizontal steel given under "Sections at the Conduit Entrance" will be seen to be conservative. Figure 2-16. Typical load division curve. Wall Thickness Change Locations Since walls of different thicknesses have different stiffnesses, the linear increase in deflection along any vertical line in the riser will be disrupted at locations where the thickness changes. Hence, vertical Analysis will show that this bending is introduced at such locations. bending is not serious and is adequately resisted by the usual amounts of T & S steel, when the changes in wall thickness are not large. Provision for Moment from Embankment Loading At closed sections. - Ordinarily the vertical steel provided for T & S As an approximate but will be adequate to resist the moment produced. quick check, the area of tensile vertical steel required in the downstream endwall may be determined conservatively as As =ggTg where A, f, D t M = = = = = total steel required, in.= 20 ksi pipe diameter, ft wall thickness, ft moment at the elevation being checked. 2-29 If this check indicates the T & S steel may be inadequate, more exact analyses can be employed before additional steel is provided. The moment may be computed as indicated M = $Fhs = 0.0125 Bh; where ft by Figure I, hS I I I I I I 1 -6 Z-17. lbs I I Figure 50 h&h, I I U use some I I Y Thus: kips B = width of endwall, f-t (for convenience, constant "weighted" width) h, = as previously defined, ft I I I I 'Z-17. wm = 5O)hs Assumed embankment loading. vertical steel, in the ends of At conduit entrance. - Extra tensile the sidewalls adjacent to the conduit entrance, may be required since the vertical downstream endwall steel is interrupted by the spigot wall The amount may be determined conservatively from the above fitting. equations, but the moment arm may need to be reduced slightly, dependThis steel will also serve ing on available room to place the steel. the additional function of providing for the pinned frame action reaction. 2-30 Stability Analyses The plan dimensions and layout of the footing must be such that the earth bearing pressure and flotation criteria, previously given, are satisfied. Various load combinations should be investigated, depending on the location of the riser relative to the embankment. As an estimate in these analyses, the thickness of the footing may be taken equal to the thickness of the riser walls immediately above the footing plus about 3”. Probably the difference, if any, between the footing thickness assumed here and the footing thickness subsequently determined by strength design, will not cause these analyses to be significantly in error. Bearing pressures may be analyzed in several ways. Because of the manner in which allowable pressures are stated, the following approach is suggested, see Figure 2-18. Q Figure 2-18. Analyses of bearing pressures. NGR =A+7 .. where MC CL!?,&-6 * - &AW2 -Aw but ..! = moment about @ of bottom of footing but not including forces, NGR = sum of vertical in the direction of M w = width of footing A = area of footing M thus %lSX. uplift +q1+&, and Paver. =- NGR A and pmin. when uplift is present: Pmin.(net) To be adequate, RIlSX. Paver. pmin. = pmin. - Pup the following where pup = 62.4~ must be satisfied: 5 allowable maximum pressure 5 allowable 10 average pressure Pmin.(net) t O Direct design for required bearing area is usually impractical because the simplest procedure is to estiNGR is a function of A. Therefore, mate A, check adequacy and revise as necessary. Riser in the Reservoir Area No endwall footing projections need to be used, required bearing area The following may be provided by using sidewall footing projections. conditions should be investigated: (1) No sediment, wind on sidewall, moist soil condition. (2) No sediment, no wind, water surface to design sediment surface. (3) No sediment, wind on sidewall, water surface to design sediment surface. (4) No sediment, no wind, water surface to crest of covered inlet. (5) Sediment to design sediment surface, no wind, water surface to design sediment surface. (6) Sediment to design sediment surface, no wind, water surface to crest of covered inlet. (7) Sediment to design sediment surface, no wind, water surface to bottom of cover slab (riser primed). (8) The flotation criteria. Revised 8-I-68 ., 2-32 Riser in the Bnbankment An upstream endwall footing projection will be used when ad'yantageous even though its use msy introduce some difficulty regarding the installation of a reservoir drain.---The following conditions should be investigated: (1) Bnbankment present, moist soil condition. (2) l3nbankment present, water surface to embankment (berm) surface. (3) Embankment present, water surface to crest of covered inlet. (4) mbankment present water surface to bottom of cover slab (riser primed j . (3) No embankment placed, moist soil condition. (6) The flotation criteria. Footing Strength Design Design is similar to that for the heel and toe of retaining walls. The footing thickness may be controlled by shear. The critical section for shear, as a measure of diagonal tension, may be taken [d] distance from the face of the riser wall, where [d] is the effective Critical footing projection loadings may be depth of the footing. determined from the various stability analyses previously listed. Note that the projection may be subjected to positive moment for some loadings end to negative moment for other loadings. Particular care should be exercised in detailing the vertical steel connecting the riser walls to the footing. When considering footing strength design with the round bottom riser, the footing support for the riser walls should probably be taken at D/4 above the pipe invert at the conduit entrance, rather than at the pipe invert elevation, to account for the variation in wall section and increased stiffness of this type of base. Thus, the moment in the footing, between the sidewalls, due to MvC and VVC is, as indicated by Figure 2-19: M = J$.ro + V&D/4 + Q/2) If desirable, due to this moment, a greater thickness than tf can be provided in the footing between the sidewalls. That is, the footing thickness between the sidewalls may be greater than the footing proThe moment expression can be modified accordingly. jection thickness. No Figure 2-19. Moment in footing NO due to vertical bending. 3-l CMER EXAMPLE DESIGN 3. Riser D Data = 30 in. Nib = 40 ft N-25 = 30 ft N,h = 10 ft Riser located in the embankment. Location of riser wall construction h, = 6.5, 11.5, 16.5, 21.5, and 36.5 f-t 26.5, 31.5, Cover joints: Slab and Cover Slab Walls Use standard design: Cover slab thickness = 8 in. Riser wall and cover slab wsll thickness = 10 in. Steel as given in Table 2-2. Layout as shown in Figure 2-2. Volume and weight - for subsequent computations: Slab - V = $(3 x 2.5 + g) (5 x 2.5 = 86.5 + f$) w= ft3 = 13.0 kips Slab walls Above crest = 29.5 ft3 w= = 4.4 kips Below crest v= 4(3 4(+-j) w= (&) ($ x (2x2.5)+ 2 x 2.5 x 2 x 2.5) = 50.0 ft3 = 7.5 kips 3-2 Riser Wall Loading As discussed in Chapter 1, the loads h, = 6.0 h, = hx h, = h, + 0.72(h, - 10) Design Wall Thickness Try t = 15 in., t/D = 3 B =( of Riser at Wall-to-Footing hx = 40 ft q = 62.4(40 + 0.72 x on the riser walls are given 0 s h, s 6.0 6.0 5 h, 5 10.0 10.0 5 h, 5 40.0 by: Walls Connection 30) = 3840 psf d = 15 - 3.5 = 11.5 in.: = 0.500 therefore KY = 1.188 l/4 1 4 x 1.188 x VITO = 3.840 x 3.70 c2.514 ) =& (1 - Ow) Mvo = 3.840 x2 (3.70)~ = 13.45 (1 - Ow) kips/ft = 23.5 ft kips/ft Shear at d above the connection: A( z)12 =0.259 gx= 3.70 e -px(cospX - [email protected]) = 0.607 e+'(singX) = 0.151 VVX = - 13.45(0.607) V - 2(23.5)(&)(0.151) . 10100 b-x = -bd = 12 x 11.5 -- 73 > 70 psi, Try t = 18 in., t/D = g =lO.l therefore kips/ft no good d = 18 - 3.5 = 14.5 in.: = 0.600 B =& vvo = 3* 840 x therefore 3.81 (1 - w) %.O = 3*840 z (30~~)~ (1 - w) KY = 1.342 = 13.8 kips/ft = 24.9 ft kips/ft Revised u-65 3-3 Shear at d above the connection: px = gi 1 (14.5) = 0.318 12 e'Bx(cosf3X - [email protected]) = 0.518 e+'(sinSX) = 0.185 VVX = - 13.8(0.518) - 2(24.9)(&)(0.185) V = 9600 = - 9.6 kips/ft = 55 < 70 ps,i, therefore 12 x 14.5 and use t = 18 in. thickness. unless horizontal OK bending requires Design for Horizontal Bendin& Table 3-l summarizes the wall thicknesses and steel Layouts will which were selected using Figure 3-l. ures 2-8 and 2-10. a greater sizes and spacings be as shown in Fig- Volume and weight - for subsequent computations: Volume of riser above footing = 86.5 Cover slab = Cover walls 79.5 Riser walls 17(38.24 lO(42.75 10(50.00 3(57*75 Weight of riser - 18.75) 18.75) 18.75) 18.75) = = = = above footing 331.3 240.0 312.5 117.0 1166.8 ft3 0.150(1166.8) = 175.0 kips Revised 11-65 II R Table Swnmary of riser 3-l. 0 hW - 10 13.5 min. use A, 10.0 16.0 10 10 - 13.5 - 17 22.0 17 - 22 30.6 10 22 - 27 39.2 12 27 - 32 47.8 15 32 - 37 56.5 15 37 - 40 57.3" 15** design for horizontal C-t-1 Steel t hX wall 10 12 15 18 75fJo f-1 Selected A, CO bending. T & S Steel Steel Selected 0.24 1.1 #%15 0.24 1.5 #?a5 0.26 1.7 #%12 0.26 2.3 #[email protected] 0.35 2.4 #% 9 0.35 3.2 #[email protected] 6 0.36 2.6 if!% 9 0.36 3.5 #[email protected] 6 0.46 3.4 #% 6 0.46 4.5 #[email protected] 6 0.38 3.1 j&2 9 0.30 4.2 #[email protected] 6 0.45 3.8 #&is 6 5.0 #[email protected] 6 0.38 3.1 #[email protected] g 0.38 4.1 #@ 6 0.45 9 As Selected 0.24 #m5 0.29 #y&2 0.36 [email protected] 0.38 [email protected]*** I * For h, = 40 - 2.5 = 37.5 ft based on load division = 15 in. if horizontal bending controlled. ** tmin. *** See following pages for design of other ,. vertical between horizontal and vertical bending. steel. . ..-. . ,. . -- . . 3-6 Vertical Steel at Wall-to-Footing Connection In sidewalls - outside steel at center of sidewalls: VVC = 13.80 kips/ft MVC = 24.9 ft kips/ft = 18 - 3.5 =14.5 in. d Direct compressive force: Weight of riser above footing = 175.0 kips Pressure = 175.0/(57.75 - 18.75) = 4.48 ksf NC = 4.48 x 18/12 = 6.72 kips/ft Analysis for required steel: d" = 1812 - 3.5 = 5.5 in. MS = 24.9 + 6.72 x 5.5/12 = 28.0 ft kips/ft thus A = 1.30 in.2/ft and As = 1.30 - 6.72/20 = 0.96 in.2/ft = $ CO Use = 3.11 in./ft = * #[email protected] (A, = 1.29, CO = 5.50) Check steel required at first construction joint: Neglect change in wall thickness from 18 in. to 15 in. 6 in. below joint, treat as though t = 18 in. gx=&i (3.5) at = 0.?2 = 0.307 e+'(sinSX) e+'(cospX + sinSX) = 0.559 MVX = - 13.8 (3.81)(0.307) + 24.9 (0.559) = - 2.3 ft kips/ft Thus, moment passes through zero a short distance below the first joint. Extend, by the use of dowels, the #[email protected] the usual lap distance above the first joint. In endwalls - inside steel at center of endwall: t/D = 18130 = 0.600 therefore KY = 0.255 B = ( 1 4 x 0.255 %o = 3.840 x 2 1l/4 x c2.514 (2.52)2 (1 -w) 1 =2.52 =11.3 f't kips/ft Revised u-65 3-7 Analysis l , .. c for required Ms = 11.3 + 6.72 x 5.5/12 = 14.4 ft kips/ft thus A = 0.64 in2/ft < required and As = 0.64 - 6.72/20 = 0.30 in2/ft for Vertical Steel for Moment from Embankment Loading Determine 'heighted" width of endwall for use in evaluating ment loadings: 7(4.17) = 29.19 lO(4.50) lO(5.00) = 45.00 = 50.00 3(5.50) = 16.50 140.69 The moment to be resisted B =140*6p T & S embank- = 4 69 ft l 30 is: M = 0.0125(4.6p)hs3 l steel: = 0.0586 hs3 f-t kips Because of the conduit entrance, the vertical T & S steel in the downstream endwall is not effective below the first construction joint, nor above it until the required embedment length is reached (taken as 2.0 ft or approximately 30 #6 bar diameters). Hence this T 8~ S steel is only checked for values of h, s 34.5 ft. Table 3-2, in which: AS = & in2 shows the analysis. Since this analysis over estimates the required steel, the usual T 8~ S steel in the downstream endwall is considered adequate for hx 5 34.5 ft even th ough the indicated required A, at h, = 34.5 ft is somewhat greater than the A, provided. Table M hS 7 12 17 l 3-2. 20 101 289 22 625 24.5 862 Vertical loading steel for moment from embankment at usual closed sections. t 3D+t 10 8.33 8.50 8.50 8.75 8.75 12 12 15 15 As 0.1 0.6 l-7 3.6 4.9 2(D+2t) 8.33 9.00 9.00 10.00 10.00 As provided 1 in2/ft/surfacc #[email protected] = 0.25 #5912 = 0.31 #[email protected] = 0.31 $46912 = 0.44 #[email protected] = 0.44 Revised ?t 1 for 11-65 T&S 3-8 For values of h, > 34.5 ft, assume the steel in the downstream 3 ft of the sidewalls is effective in resisting the moment and use (3D + t/2) as the moment arm. Thus for h(-.) = 40 ft: h, = 30 ft M = 1580 ft kips A, = 'm Provided I 1580 = 9.6 in.2 by inside steel for T ??cS: #[email protected] = 0.44 x 3 x 2 = 2.6 in.2 Provided by outside steel for vertical bending #[email protected] = 1.20 x 3 x 2 = 7.2 in.2 Total area provided = 9.8 in.?, Stability Preliminaries Volume outside riser mum) section: Between footing 7(57.75 - 38.24) lO(57.75 - 42.75) lO(57.75 - 50.00) 3(57.75 - 57.75) v, Between earth surface 10(57.75 - 38.24) slab walls . .-., v2 Displacement volume slab walls 17(38.24) lO(42.75) 10(50.00) ..-, 3(57.75) Rough, preliminary with a thickness dimensions, Analyses wsJls but inside and earth = = = OK 5.5 x 10.5 (the msxi- the projected surface: 136.6 150.0 77.5 0.0 = = 364.1 f-t? and crest of covered inlet: = 195.1 = - 50.0 = 145.1 fte of riser between footing = and crest of covered inlet: 50.0 = 650.1 = 427.5 = 500.0 = 173.2 VD = 1800.8 fts computations indicate a footing Figure of 21 inches is required. of about 16 ft x 14 ft 3-2 shows the trial 3-9 Thus, for the footing: = 224 ft2 Area Volume = 392 ft3 Weight = 58.8 kips and the various working volumes: vB1 = 30(2 VB; = (lo/301 x 4.25 x 10.5) = 2680 = vBl ft3 have taken the ft3 for the slab walls from VB' instead 1 of from V2, or could have taken it partly from both.) 893 ft3 = 30(5.5 x 14) = 2310 ft3 VB; = (lo/3a) vB2 = 770 ft3 vB2 (Could 50.0 16.0 5.5 10.5 I 7 f/ /I ,I // ,C , 4.25 ,I A c. g. of ftg. 5.5 riser less / / / / // / L 1 2.75 1 2.75 5.25 5.25 -I Figure 3-2. Plan of trial footing. 7, Ii 4.2: 3-10 eF= Embankment present, moist soil conditions: Allowable average pressure = 0.140 x 31.75 + 2.00 = 6.44 ksf Allowable maximum pressure = 0.140 x 31.75 + 4.00 = 8.44 ksf Weighted wsll width = 4.69 ft. Embankment moment: M= 0.0125 x 4.69 x (31.75)' = 1875 ft kips Riser less footing = 175.0 x (- 2.75) = - 481 Footing VI = 364.1 x 0.14 vB1 = 2680 x 0.14 QB2 = 2310 x 0.14 = = = = 58.8 x ( 0 > = 0 51.0 x (- 2.75) = - 140 375.0 x (- 2.75) = - 1030 323.0 x (+ 3.25) 982.8 kips Moment about * of footing: M$ = 1875 + 44 = 1919 ft kips )= 4.3g(i.733) pmax. =~(++$!j (2) Paver. = 4.39 < 6.44 ksf, Pmin. = 4.39(0x67) Paver. pmin. puplift pmin. (net) (3) kips = 7.62 < 8.44 ksf, = 1.17 > 0 ksf, OK embankment (berm) surface: 31.75 +l.OO = 5.44 ksf 31.75 + 2.00 = 6.44 ksf kips kips = -3 ;"2 (1 + l; ; ';;;) = 4.3g(1.446) = 4.39 < 5.44 ksf, OK = 4.39(0.554) = 2.43 > 0 ksf, OK = 0.0624 x 31.75 = 1.98 ksf = 2.43 - 1.98 = 0.45 > 0 ksf, = 6.35 < 6.44 ksf, OK Ebnbankment present, water surface to crest of covered inlet: Allowable average pressure = 5.44 + 10 x 0.0624 = 6.06 ksf Allowable maximum pressure = 6.44 + 10 x 0.0624 = 7.06 ksf Previous =982.8 + 44 v2 = 145.1 x 0.0624 VB; = 893 x 0.0624 VB; = 770 x 0.0624 OK OK Embanlunent present, water surface to Allowable average pressure = 0.140 x Allowable maximum pressure = 0.140 x M = (30/50)(1875) = 1125 ft = 1125 + 44 = 1169 ft W b.X. = + 1695 -t 44 ft = 9.1 x (- 2.73) ==- 25 = 55.7 x (- 2.75) = - 153 = 48.0 x (+ 5.25) = + 252 1095.6 kips + 118 ft kips OK 3-11 . (4) w = &lax. = g Paver. Pmin. puplift Pan(net) = 4.90 < 6.06 ksf, OK = b.gO(O.575) = 2.82 > 0 ksf, = 0.0624 x 41.75 = 2.60 ksf = 2.82 - 2.60 = 0.22 > 0 ksf, U.25 + 118 = 1243 f-t kips (1 + -m) = 4.90(1.425) Embankment present, water surface (riser primed): Allowable average pressure = 5.44 Allowable maximum pressure = 6.44 Previous = logy.6 Water in riser 40 x 18.75 x 0.0624 = 46.8 Water over crest 224 x 1.25 x 0.0624 = 17.5 Slab wsJls above crest - 29.5 x 0.0624 = -1.8 = 7.00 < 7.06 OK OK to bottom of cover + 11.25 x 0.0624 + 11.25 x 0.0624 0 % = ll25 &IlSX. = z (1 + li > paver. = = = = Pmin. puplift Pmin. (net) (5) = 5.17(1.362) 5.17 < 6.14 ksf, OK 5.17(0.638) = 3.30 > 0 ksf, 0.0624 x 43.0 = 2.68 ksf 3*30 - 2.68 = 0.62 > 0 ksf, = 0 = + 5 - 1158.1 ; ;$;) ksf ksf = - 129 x (- 2.75) kips - 6 = 1119 ft kips slab = 6.14 = 7.14 = +n8 x (- 2.75) x ( ksf, OK 6 ft kips = 7.05 < 7.14 ksf, OK OK OK No embankment placed, moist soil condition: Allowable average pressure = 0 + 2.00 = 2.00 ksf Allowable maximum pressure = 0 + 4.00 = 4.00 ksf Riser less footing = 175.0 x (- 2.75) = - 481 Footing = 58.8 ( 0 >= 0 233.8 kips w = - 481 ft kips %lS. z&l+ Paver. pmin. = 1.05 ksf < 2.00 ksf, OK = 0.24 3 0 ksf, = 1.05(0.230) ~$$+$-) - 481 ft = 1.05(1.770) kips = 1.85 < 4.00 ksf, OK OK Revised 8-l-68 3 -12 (6) Flotation criteria: Will not count on buoyant weight of submerged embankment over footing projections unless needed. weight of riser 233.8 m weight of displaced water = 1800.8 + 392) 0.0624 =137.0 = 1.7 > 1.5, OK Use 16 x 14 footing. Footing Projection Loadings The projection loadings ity analyses. (1) Upstream Downstream (2) u D (3) u D (4) u D (5) u D Design Check on footing In downstream Shear: Strength are tabulated Design in the same order as the stabil- (7.62) - (l-75 x 0.15 + 30 x 0.14 = 4.46) (1.17) - (4.46) (6.35) - (4.46) (2.43) - (4.46) (7.00) - (4.46 + 10 x 0.0624 = 5.08) (2.82) - (5.08) (7.05) - (5.08 + 1.25 x 0.0624 = 5.16) (3.30) - (5.16) (0.24) - (1.75 (1.85) - (0.26) x 0.15 = 0.26) thickness required: end of sidewall footing d = 3290(4.25 projection: - d/12) 70 x 12 d = 12.6 in. = 29.7 ft kips/ft Moment: M = 3.29(4.25)*/2 d = 10.5 in. for balanced stresses tf z 12.6 + 2.5 = 15.1 in. In upstream endwsll footing projection: Pressure at face of endwall: P = 3.16(X*23) thus x = 7.85 ft where x = (-ha) . and p = 0.95 ksf 16 = = = = 3.16 ksf t 3.29 J t 1.89 2.03 4 = 1.92 t = 2.26 = 1.89 = 1.86 $ P 4 = 0.02 = 1.59 s t 3-13 a Shear: d N (31.60 + 950) (5.5 - d/12) 70 x 12 2 d -11.2 , h in. + 2.2I~(5.5)~/3 = 36.6 ft kips/ft M = o.95(5.5)*/2 d = 11.7 in. for balanced stresses 2 11.7 + 4.5 = 16.2 in. Moment: tf Assumed thickness is OK, use tf = 21 in. Determine footing steel required: T & S requires A,(min.) = 0.002 x 12 x 16 = 0.38 in*/ft Design of transverse steel (perpendicular to sidewall): Top steel: d = 21 - 2.5 = 18.5 in. Downstream: M = 29.7 ft kips/ft As = 1.05 in*/ft co IT= 3290 x 4.25 = 3.53 in./ft 245 x 7/8 x 18.5 Because of the unknown thickness of the spigot wall fitting, this steel should not be placed under the fitting but should In order to provide the be started ahead of the fitting. the maximum area required per foot same total resistance, will have to be increased to: 1.29 in.*/ft & =1.05 Use short length ##&?12, A, = 0.44 in.*/ft each side of fitting to provide for T & S. Use #E&4, A, = 1.33 in.2/ft for 2.5 ft Use #6??8, A, = 0.66 in.*/ft for starting ahead of fitting. next 2.5 ft, then use #@12. Upstream: Use #&112, A, = 0.44 > 0.38 in.2/ft Bottom steel: d = 21 - 3.5 = 17.5 in. Downstream: M = 1.59(4.25)*/2 A, = 0.53 in.*/ft = 14.4 ft kips/ft 1590 x 4.25 =O = 350 x 7/t] x 17.5 = 1.26 in./ft Use #f&6, A, = 0.88 in.*/ft. Co = 4.71 in./ft, Change to #[email protected] at 16 - 16(0.44/0.53) = 2.7 say 3 ft from downstream end of footing. Upstream : Use#[email protected], As = 0.44 > 0.38 in.*/ft Revised 8-l-68 3-14 Design of longitudinal steel (perpendicular to end-wall): Top steel: d = 21 - (2.5 f 1.0) = 17.5 in. Use #6912, As = 0.44 > 0.38 in.'/ft Bottom At M A, steel: d = PII- - (3.5 + 1.0) = 16.5 in. face of upstream endwall: = 36.6 ft kips/ft = 1.48 in.;?/ft + Ooy5) (5.5) 2 V = (3*16 Co = 350 x 11300 718 x 16.5 = 11.3 kips = 2.24 in./ft Use #[email protected] and #f&2, As = 1.64 in.2/ft, Co = 7*86 in./ft. Drop the #[email protected] at anchorage distance downstream qf the downstream face of endwall. Design of footing steel for MVo and VVo: At center of sidewall: MVO = 24.9 ft kips/ft, VVo = 13.8 kips/ft Assume two layers of steel: = 21 - (3.5) - (1.0) = 16.5 in. d = 6.0 in. d" = 21/2 - 4.5 %. + vvo (t +-F) = 24.9 +13.8 VVo d"/12 = 13.8 (0.625 + 0.875) = 45.6 (6.0/d = 6.9 M, A = 2.15 in.2/ft A, = 2.15 - 13.8/20 = 52.5 ft kips/ft = 1.46 in2/ft #[email protected] (continuous #@Z&2 (place from sidewall to footing to sidewall)= 1.20 = 0.44 the #[email protected] 2 in. above this steel) 1.64 > 1.46 in2/ft Example Plans PlEUM, for consisting of a layout sheet and three structural detail sheets, the riser designed in this example are shown on the following pages. ... ,. -. ,” .._. E-E -- N01133S n3sI~ 03~3~03 auvpws SNVld 3ldWVi3 V-V NOl133S .133HS 33s 9Nl1 VET ON V 5379NV 213v&ww,y1 JO 7/K&w No, NW-Id d01 ” _- w 9 ifii - 1 t9 5TEEL STEEL Z” FROM i-O,= OF SLAB STEEL 2” FRaM BOTTOM OF SLAB COVER SLAB PLAN RISER WALL STFELNOTWOWN E’FROM SECTION INSIDE FACE B-B re CUTSlOE FACE /NSlDE FACE SECTION A-A STEEL 2” FROM OUTSIDE FACE ENDWALL STEEL Z-FROM lN5lDE COVER 5LAU STEEL NOT SHOWN BAR TYPES 5m. FACE STEEL 2” FRO?., OUTSIDE SECTION ELEVATION TYPE I 5-B FACE

Download PDF

advertisement