Modular Box Engineering
Exterior (Cp) Coefficients
Figure D - 4
a. The Gust Response Factor (Gh) is assumed to be based on Exposure C (see section D‑200.4.C.1.c). The Minimum Property Standard (MPS) permits use of Exposure C regardless of whether the site is inland or coastal. Thus, for units of assumed mean height less than or equal to 15 feet, Gh = 1.32.
b. External Roof and Wall Pressure Coefficients (Cp) vary on the windward roof surface based on the structural issue being analyzed. Figure D‑4 illustrates the various (Cp) values for the transverse and longitudinal directions. A roof slope of 10 to 15 degrees ( 2 in 12 to 3 in 12) produces 2 possible situations: (+0.2) pressure and (‑0.9) suction. The value (‑0.9) was selected to produce maximum suction for uplift and overturning while (+0.2) was selected to maximize sliding. Note that (+) means pressure on the external surface, while (‑) means suction on the external surface. For the leeward wall in the longitudinal direction the proportions of the unit (L/Wt) are important to establishing the proper exterior (Cp) value. Single-section units, regardless of the combination of width or length, has a ratio L/Wt ³ 4.0; therefore, Cp = -0.2. For multi-section units An average proportion of unit (28’ x 70’, or 32’ x 80’) was assumed. Thus, the L/Wt ratio was 2.5 and by interpolation Cp = -0.275. Single or multi-section units have a Wt/L ratio, which is £ 1.0 for all proportions of units. Thus, the leeward value for Cp = -0.5 in the transverse direction.
A. Gravity Load Considerations for the Type C Single-Section Unit.
1. General: The foundation to support the superstructure gravity loads is provided only by the spaced piers under the chassis beams.
2. Superstructure load to a pier: As shown in Figure D 8A the snow load, the attic live load and the roof dead load are transferred equally to each exterior wall. The exterior walls in turn transfer the roof loads to the floor framing. The floor live and dead load combine with the roof and wall load to reach the chassis beam, where the foundation piers receive the total concentrated super-structure load (Rp) in proportion to the pier spacing.
3. Typical chassis beam pier founda-tion weight: The typical pier as-sumed for the calculations is based on a pier composed of four 8”x8”x16” concrete masonry units grouted solid with a 2 foot square footing that is 8 inches deep. Thus the assumed pier weight is as fol-lows:
pier: 2.67’ 1.33’ 84 psf = 298.0 lbs.
footing: 150 pcf 2’ 2’ .67’ = 402.0 lbs.
total = 700.0 lbs.
4. Required chassis beam Pier Footing size: The footing area (Aftg) must be large enough so that the net al-lowable soil bearing pressure (Pso) is not exceeded under the full grav-ity dead, live and snow loads. Note that the pier and footing weight be-come additional dead load.
B. Gravity Load Considerations for the Type E and I Single-Section Unit.
1. General: Support of the superstruc-ture gravity loads is shared by the exterior longitudinal walls and the spaced interior piers under the chas-sis beams, which together comprise the foundation.
2. Superstructure load to the exterior longitudinal foundation walls: As shown in Figure D 8B, the snow load, the attic live load and the heavy roof dead load are transferred equally to each exterior wall. The exterior wall weight is added, and both loads transfer directly to the exterior foundation walls. A portion (dc/2) of the floor live and heavy dead load also goes to the exterior foundation walls. The total super-structure gravity load (Rw) trans-ferred to the exterior foundation wall is in units of lbs./ft. of home length. The equation is as follows:
[snow + (roof DL+attic LL)]
(floor LL+DL) + (wall DL)
3. Superstructure load to an interior pier: The remainder of the floor dead and live load is equally divided between the chassis beam lines, and concentrated at the foundation piers based on their spacing. The total superstructure concentrated gravity load to a pier (Rp) is as follows:
(floor DL+LL) (chassis beam DL)
Gravity Loads
Figure D -8B
4. Typical exterior longitudinal foun-dation wall weight: The typical ex-terior longitudinal foundation wall is assumed to be composed of a 6” poured concrete wall, 3’-8” high, and a 6” x 24” continuous concrete footing. Thus, the assumed weight is as follows:
wall: 150 pcf 3.67’ 0.5’ = 275.0 plf
footing: 150 pcf 2’ 0.5’ = 150.0 plf
total = 425.0 plf
5. Required Exterior Wall Footing Width: The footing width (Wf) must be large enough so that the net allowable soil bearing pressure (Pso) is not exceeded under the full grav-ity dead, live and snow loads. Note that the longitudinal foundation wall and footing weight become addi-tional dead load. The required foot-ing width:
6. Required Interior Pier Footing Area: The footing area (Aftg) must be large enough so that the allow-able soil bearing pressure (Pso) is not exceeded under the full gravity dead and live loads. Note that the pier and footing weight become ad-ditional dead load. The required footing area:
C. Gravity Load Considerations for the Type C Multi-Section Unit with a Continu-ous Superstructure Marriage wall.
Type C - Multi-Section Unit w/Continuous Marriage Wall
Figure D - 9A
1. General: The foundation to support the superstructure gravity loads is provided only by spaced piers under the chassis beams and under the continuous marriage wall.
2. Superstructure continuous marriage wall load to a pier: As shown in Figure D 9A the snow load, the attic live load and the roof dead load are transferred between the marriage wall and the exterior walls as bear-ing walls. The marriage wall in turn transfer the roof loads to the floor framing. A small portion of the floor live and dead load is assumed to combine with the roof loads and marriage wall weight to reach the top of the foundation pier as the to-tal concentrated superstructure load (Rpm) in proportion to the pier spacing.
marr.wall+(snow+roofDL+attic LL)
(floor DL+LL)
3. Superstructure load to an exterior chassis beam pier: As shown in Figure D 9A the snow load, the attic live load and the roof dead load are transferred equally between the ex-terior wall and the marriage wall. The exterior wall in turn transfers the roof loads to the floor framing. The floor live and dead load com-bine with the roof and wall weight to reach the chassis beam, where the foundation piers receive the total concentrated superstructure load (Rpe) in proportion to the pier spac-ing.
snow+roofDL+atticLL+floorDL+LL
(ext.wall DL+chassis bm.)
4. Superstructure load to an interior chassis beam pier: As shown in Figure D 9A The floor live and dead load comprise the only load to reach the interior chassis beam, where the foundation piers receive the total concentrated superstructure load (Rpi) in proportion to the pier spac-ing.
[(floorLL+DL)+chassis bm.]
5. Typical Continuous Marriage Wall Pier: The typical continuous mar-riage wall within the superstructure of the multi-section unit is assumed to have a foundation pier composed of five courses of 8”x8”x16” con-crete block (ungrouted), and a con-crete footing 2’x2’ by 8” deep. The dead load of a typical continuous marriage wall foundation pier is as follows:
pier: 42 psf 3.33’ 1.33’ = 186.0 lbs.
footing: 150 pcf 22 .67’ = 402.0 lbs.
total = 588.0 lbs.
6. Required continuous marriage wall pier footing. The footing area (Aftg) must be large enough so that the net allowable soil bearing pres-sure (Pso) is not exceeded under the full gravity dead, live and snow loads. Note that the pier and foot-ing weight become additional dead load. The required footing area:
7. Required exterior chassis beam Pier Footing Area: The footing area (Aftg) must be large enough so that the allowable soil bearing pressure (Pso) is not exceeded under the full gravity dead and live loads. Note that the pier and footing weight be-come additional dead load. The re-quired footing area:
8. Required interior chassis beam Pier Footing Area: The footing area (Aftg) must be large enough so that the allowable soil bearing pressure (Pso) is not exceeded under the full gravity dead and live loads. Note that the pier and footing weight be-come additional dead load. The re-quired footing area:
D. Gravity Load Considerations for the Type C Multi-Section Unit with a Super-structure Marriage wall containing one opening or two large adjacent openings.
Type C - Multi-Section Unit w/Openings in Marriage Wall
Figure D - 9B
1. General: The foundation to support the superstructure gravity loads, as illustrated in Figure D-9B, is pro-vided only by spaced piers under the chassis beams, piers placed under the posts at the ends of marriage wall openings, and equally spaced piers under the continuous portions of the marriage wall.
2. Marriage wall openings: limitations and assumptions. Two marriage wall opening situations were re-viewed: (1) a single opening, as il-lustrated in Figure D-9C, is bounded by posts at the ends of the opening with continuous marriage walls ex-tending beyond the opening width in both directions, and (2) two adja-cent marriage wall openings, as il-lustrated in Figure D-9D, consisting of three posts with the outer two posts having continuous marriage walls extending beyond the two openings.
Note: A maximum 10 foot pier spacing was assumed under all con-tinuous marriage wall portions.
Note: The center post between the two adjacent openings of the later scheme produces the largest con-centrated load to a marriage wall pier. This is the condition used for the equations that follow.
Note: It is conservatively assumed that the footing size required under the center post will be used under all three posts in the Appendix B Part 1 Tables for Multi-section units.
Marriage Wall w/Large Single Opening
Figure D - 9C
Note: The opening width used for two adjacent openings in the Ap-pendix B Tables, is the average of the two opening widths: (x+x1) 2. The marriage wall opening tables use 2 foot increments for single openings, or the average of two ad-jacent openings, from 10 feet to 20 feet.
3. Superstructure: Two large adjacent marriage wall openings: load to the pier under center post: As shown in Figure D 9D the snow load, the attic live load and the roof dead load are transferred between the marriage wall ridge beam and the exterior walls as bearing points. The mar-riage wall ridge beam (assumed to act as two simple span beams) trans-fers the average of the two opening widths of the roof and attic loads to the center post. The floor live and dead load is assumed to be carried by floor beams, and also is trans-fered based on the average width of the two openings.
Marriage Wall w/Two Adjacent Openings
Figure D - 9D
Note: For a single opening x1=0 and all the formulas still work.
The floor beam is assumed to weigh 10 plf and the ridge beam is assumed to be composed of 6 layers of 3/8”plywood at a depth of 3 feet. Thus, the ridge beam weighs 19.8 plf. The post is assumed to be a 4x4 of weight 32 lbs. The total concen-trated superstructure load to the pier (Rmax):
( snow+roofDL+attic LL)
(floor DL+LL)+floor bm+Ridge bm ) +post DL
4. Superstructure load to an exte-rior chassis beam pier: the super-structure load to an exterior pier is unchanged from that for a Type C multi-section unit with a continuous marriage wall. Thus, the total con-centrated superstructure load (Rpe) is repeated here:
snow+roofDL+atticLL+floorDL+LL
(ext.wall DL+chassis bm.)
5. Superstructure load to an interior chassis beam pier: the superstruc-ture load to an interior pier is un-changed from that for a Type C multi-section unit with a continuous marriage wall. Thus, the total con-centrated superstructure load (Rpi) is repeated here:
[(floorLL+DL)+chassis bm.]
6. Required pier footing area for mar-riage wall containing large open-ings. The footing area (Aftg) must be large enough so that the net al-lowable soil bearing pressure (Pso) is not exceeded under the full grav-ity dead, live and snow loads. Note that the pier and footing weight be-come additional dead load. The re-quired footing area:
7. Required pier footing areas for ex-terior and interior chassis beam lines. See items 7 and 8 for a Type C Multi-section unit with a continu-ous marriage wall. Equations are the same and are repeated here for ease of use:
E. Gravity Load Considerations for the Type E and Type I Multi-Section Unit with a Continuous Superstructure Marriage Wall.
1. General: As illustrated in Figure D 9E, the foundation to support the superstructure gravity loads is pro-vided by spaced piers under the chassis beams, along the exterior wall and by spaced piers under the continuous marriage wall.
Note: Foundation Concepts E5 and E7 do not follow the equation development presented here and are treated sepa-rately, later in Section D.300.1.
Type E and I - Multi-Section Units w/Continuous Marriage Wall
Figure D - 9E
2. Superstructure continuous marriage wall load to a pier: Identical to that shown in Figure D 9A for the Type C multi-section unit; the snow load, the attic live load and the roof dead load are transferred between the marriage wall and the exterior walls as bearing walls. As shown in Fig-ure D-9E the marriage wall in turn transfers the roof loads to the floor framing. A small portion of the floor live and dead load is assumed to combine with the roof loads and marriage wall weight to reach the top of the foundation pier as the to-tal concentrated superstructure load (Rpm) in proportion to the pier spacing.
marr.wall+(snow+roofDL+attic LL)
(floor DL+LL)
3. Superstructure load to an exterior and interior chassis beam pier: As shown in Figure D-9E there are no gravity roof loads or exterior wall load transferred to the piers under the chassis beams. The floor live and dead load comprise the only load to reach the exterior and inte-rior chassis beam, where the exterior and interior foundation piers receive the total concentrated superstructure load (Rpe and Rpi) equally in pro-portion to the pier spacing.
( floorDL+LL) (chassis bm.)
4. Superstructure load to the exterior foundation wall. As shown in figure D-9E the snow load, the attic live load and the roof dead load are transferred equally between the ex-terior wall and the marriage wall. The exterior wall in turn transfers the roof loads to the floor framing. A small portion of the floor live and dead load combine with the roof and wall weight to reach the foundation wall as a lineal uniform load (Rw).
5. Required continuous marriage wall pier footing. The footing area (Aftg) must be large enough so that the net allowable soil bearing pres-sure (Pso) is not exceeded under the full gravity dead, live and snow loads. Note that the pier and foot-ing weight become additional dead load. The required footing area:
6. Required exterior and interior chassis beam Pier Footing Area: The footing areas (Aftg) must be large enough so that the allowable soil bearing pressure (Pso) is not ex-ceeded under the full gravity dead and live loads. Note that the pier and footing weight become addi-tional dead load. The required foot-ing areas:
7. Required exterior foundation wall Footing Width: The footing width (Wf) must be large enough so that the allowable soil bearing pressure (Pso) is not exceeded under the full gravity dead and live loads. Note that the wall and footing weight be-come additional dead load. The re-quired footing width becomes:
F. Gravity Load Considerations for the Type E and I Multi-Section Units with a Su-perstructure Marriage wall containing one opening or two large adjacent openings.
1. Continuous marriage wall. The equation development presented in Section D.300.1.E for loads and footing sizes at exterior foundation wall and exterior and interior chassis beam line piers is identical to that when a continuous marriage wall ex-ists and will not be repeated here.
2. One opening or two adjacent open-ings. The considerations for the foundation piers under the posts that define one opening, or two adjacent large openings within the length of the continuous marriage wall, is the same as that for the Type C Multi-section unit presented in Section D.300.1D and illustrated in Figure D-9D. The equation for the maxi-mum reaction under the center post will be repeated here:
( snow+roofDL+attic LL)
(floor DL+LL)+floor bm+Ridge bm ) +post DL
Note: For a single opening x1 = 0 and all the equations still work.
3. Required marriage wall pier footing at center post. The pier and footing weight become additional dead load. The required footing area under the center post location repeats also:
Note: Regardless of Multi-Section Unit Type C, E or I the equations developed for piers under the con-tinuous marriage walls and the equa-tions developed for the pier under the center post, when two large marriage wall openings exist, do not change. The only exception is for the Type E5, (E6 uses E5 Tables) and E7 Multi-section units, which are presented further on in this Sec-tion D.300.1.
G. Gravity Load Considerations for the Type Cnw Multi-Section Unit with a con-tinuous marriage wall (without any mar-riage wall piers).
1. General: As illustrated in Figure D 9F, the foundation to support the superstructure gravity loads is pro-vided by spaced piers under the ex-terior and interior chassis beams. Note: A marriage wall with large openings is not considered feasible for this foundation concept, since it would require piers under the posts.
2. Superstructure load to an interior or exterior chassis beam pier: Simi-lar to that shown in Figure D 9A for the Type C multi-section unit; the snow load, the attic live load and the roof dead load are transferred be-tween the marriage wall and the ex-terior walls as bearing walls. The marriage wall and the exterior wall in turn transfer their dead weight and the roof loads to the floor fram-ing. The floor live and dead load is equally distributed each chassis beam line. These loads from both levels combine to reach the top of the foundation pier as the total con-centrated superstructure load (Rp) in proportion to the pier spacing.
Note: The only difference between the exterior pier load and the inte-rior pier load is in the difference of the weight of the exterior wall and marriage wall. Since the exterior wall has a greater weight that the marriage wall, it will be used and thus the load to the exterior and in-terior chassis beam piers will be as-sumed equal.
Type Cnw - Multi-Section Units w/Continuous Marriage Wall
Figure D - 9F
3. Required exterior and interior chassis beam Pier Footing Area: The footing area (Aftg) must be large enough so that the allowable soil bearing pressure (Pso) is not ex-ceeded under the full gravity dead and live loads. Note that the pier and footing weight become addi-tional dead load. The required exte-rior and interior footing areas be-come:
H. Gravity Load Considerations for the Type E5 Multi-Section Unit with a Continu-ous Superstructure Marriage Wall.
1. General: As illustrated in Figure D 9G, the foundation to support the superstructure gravity loads is pro-vided by spaced transverse steel girders (under the chassis beams) that span between pilasters built into the exterior foundation walls and by spaced piers under the continuous marriage wall. A crawlspace exists below the first floor. The transverse steel girder is assumed to be com-posed of two simple spans that run from exterior wall to the central marriage wall piers, rather than cre-ate a continuous two span girder.
Type E5 Multi-Section Units w/Continuous Marriage Wall
Figure D - 9G
Note: A licensed professional shall be re-sponsible for the design of the trans-verse steel girders.
2. Superstructure floor load trans-ferred to the transverse steel girder and then to the exterior foundation wall pilaster. As shown in Figure D 9G the floor dead and live load transfer to the chassis beam lines and present concentrated loads to the transverse girder. This concen-trated load is then assumed to trans-fer to the end of the transverse girder and bear on the pilaster. Based on the transverse girder spac-ing, the concentrated load (F1) be-comes:
(floorLL+DL)
3. Superstructure load to the exterior foundation wall: As shown in Fig-ure D-9G the snow load, the attic live load and the roof dead load are transferred between the marriage wall and the exterior walls as bear-ing walls. The exterior wall trans-fers this load down to the top of the foundation wall. A small portion of floor load is assumed to also go to the foundation wall. This is a uni-form linear load (F2) as follows:
(snow +roof DL+atticLL)
(floorLL+DL) (exterior wallDL)
4. Superstructure total load to the ex-terior foundation wall: As shown in Figure D-9G the pilaster receives load (F1) and this load plus the transverse girder weight of 20 plf spreads at a 45 angle along the wall length based on an assumed wall depth of 2 feet. Therefore, the spread in the wall is 4 feet. This spread load combines with the roof and exterior wall load (F2) to pro-duce a total reaction (Rw) to the footing as follows:
5. Superstructure load at the marriage wall: As shown in Figure D-9G the snow load, the attic live load and the roof dead load are transferred be-tween the marriage wall and the ex-terior walls as bearing walls. The continuous marriage wall transfers this load down to the floor level and to a short steel post as a concen-trated load, based on the spacing of the transverse girders. This concen-trated load (F3) is as follows:
(snow +roofDL+LL) (marriage wall weight)
(floor DL+LL)
6. Superstructure total load to a con-tinuous marriage wall pier: As shown in Figure D-9G two concen-trated floor loads (F1) plus the con-centrated load (F3) in addition to the transverse girder weight of 20 plf are assumed to be transferred to the continuous marriage wall pier as a total concentrated load (Rpm) as follows:
7. Required exterior foundation wall Footing Width: The footing width (wf) must be large enough so that the allowable soil bearing pressure (Pso) is not exceeded under the full gravity dead and live loads. Note that the wall and footing weight be-come additional dead load. The re-quired footing width becomes:
Note: The width of the footing be-tween pilasters is assumed to be the same as at the pilaster. It is uneco-nomical to continually jog footing forms. Plus the spread through the wall will almost encompass the the entire wall between pilasters any-way.
8. Required continuous marriage wall pier footing. The footing area (Aftg) must be large enough so that the net allowable soil bearing pres-sure (Pso) is not exceeded under the full gravity dead, live and snow loads. Note that the pier and foot-ing weight become additional dead load. The required footing area:
I. Gravity Load Considerations for the Type E7 Multi-Section Unit with a Continu-ous Superstructure Marriage Wall.
Type E7 Multi-Section Units w/Continuous Marriage Wall
Figure D - 9H
1. General: As illustrated in Figure D 9H, the load flow of the super-structure gravity loads is identical to that for the Type E5 multi-section unit, and the equation development is very similar. The only difference is that instead of a crawlspace, a full basement exists below the first floor. Thus, the exterior foundation is a full depth basement wall and footing with space pilasters. Again, the transverse steel girder is assumed to be composed of two simple spans that run from exterior basement wall to the central marriage wall, where steel pipe columns and a spread footing are used instead of piers.
Note: A licensed professional shall be re-sponsible for the design of the basement wall for gravity loads and lateral earth pressures; as well as the transverse steel girders and the steel pipe column.
2. Exterior foundation basement wall and footing assumptions. A 6’-8” headroom is assumed under the transverse girders that are assumed to be 12 inches deep. The chassis beams are assumed to be 10” deep. Thus, the total wall height to the top of basement floor is 8’-6”. To maximize the gravity loading the walls are assumed to be 8 “ solid concrete, rather than the also ac-ceptable reinforced concrete block. The linear footing proportions are set at 1 foot deep x 2 feet wide. Since the pilaster only exists at the spacing of transverse girders its weight has been ignored. The foun-dation dead load becomes:
Conc. wall: 0.67’ 8.5’ 150 pcf = 850 plf
footing: 1.0 2.0 150 pcf = 300 plf
total = 1150 plf
3. Foundation under the marriage wall: Steel pipe columns 3.5” are assumed spaced under the transverse girders with a base plate at the bot-tom and a cap plate at the top with holes for bolting. The footing is as-sumed to be 1’deep x 3’ x 3’. The column/footing load is therefore:
Column: 7.6 plf 7 feet tall = 54 lbs.
Footing: 150pcf1’3’3’ = 1350 lbs.
total = 1404 lbs.
4. Superstructure floor load transferred to the transverse steel girder and then to the exterior foundation wall pilaster. The load (F1) is identical to that for the Type E5 Multi-Section unit found in section D.300.1.H.2.
5. Superstructure load to the exterior foundation wall: The load (F2) is identical to that for the Type E5 Multi-Section Unit found in section D.300.1.H.3.
6. Superstructure load at the marriage wall: The load (F3) is identical to that for the Type E5 Multi-Section Unit found in section D.300.1.H.5.
7. Superstructure total load to the ex-terior foundation wall: The pilaster receives load (F1) and the transverse girder weight of 20 plf. This load spreads at a 45 angle along the wall length based on an assumed wall depth of 8’-6” below the superstruc-ture. Therefore, the spread in the wall would be greater than the maximum 10 foot spacing for trans-verse girders. The maximum Code prescribed spread is thus the spacing (s). This spread load combines with the roof and exterior wall load (F2) to produce a total reaction (Rw) to the footing as follows:
8. Superstructure total load to a con-tinuous marriage wall pier: The to-tal concentrated load to the steel pipe column is identical to that for the Type E5 Multi-section unit con-centrated load to a pier, found in section D.300.1.H.6. The total con-centrated load (Rpm) is repeated here as follows:
9. Required exterior foundation wall Footing Width: The footing width (wf) must be large enough so that the allowable soil bearing pressure (Pso) is not exceeded under the full gravity dead and live loads. Note that the wall and footing weight be-come additional dead load. The re-quired footing width becomes:
10. Required continuous marriage wall pipe column footing. The footing area (Aftg) must be large enough so that the net allowable soil bearing pressure (Pso) is not exceeded under the full gravity dead, live and snow loads. Note that the steel column and footing weight become addi-tional dead load. The required foot-ing area:
11. Basement longitudinal beams used to space steel pipe columns further apart: It would be possible to add longitudinal steel beams to support the transverse steel girders in order to avoid a large number of pipe col-umns. This produces concentrated loads to the longitudinal beams, which could be spaced (b) distance apart, assuming (b)(s) by a signifi-cant amount. The value (n) is the number of transverse beams that oc-curs within the distance (b). The area of footing would then become:
Note: There are no tables in Appendix B to cover this situation. The steel pipe column, the transverse and lon-gitudinal steel beams would require design by an engineer.
J. Gravity Load Considerations for the Type E5, E6 and E7 Multi-Section Units with a Superstructure Marriage Wall con-taining one opening or two large adjacent openings.
1. General: The presence of regularly spaced steel transverse girders in these foundation concepts compli-cates the equation development to account for randomly placed large openings along the marriage wall line. Any concentrated post load, defining the ends of an opening, that falls between transverse girders would require either another pier or column, that would in many cases be close enough to the grid of trans-verse girder piers and posts, as to overlap or abut- clearly uneconom-ical and impractical to construct.
2. Marriage wall openings: assump-tions and limitations: It has been assumed and is now recommended in this Handbook, that opening widths for these three foundation concepts be a multiple of the trans-verse girder spacing for the practical reasons stated above. Any other as-sumptions would require the design of a licensed professional.
The equation development will again follow the logic and assumptions of Section D.300.1.D.2 and will not be repeated here. Thus, two adjacent openings will be considered, with the center post receiving the largest concentrated load. All three post lo-cations will have their foundation sized based on that center post, thus introducing a degree of conserva-tism.
The equations for the exterior foun-dation footing width are identical to those of the individual concepts for the Type E5 (E6 uses E5) and E7 already developed for a continous marriage wall, and will not be re-peated here.
3. Roof load to a center post between two large marriage wall openings: The given situation, illustrated in the roof plan of Figure D-9I, shows two adjacent marriage wall openings that follows the assumption of openings being a multiple of the transverse girder spacing; one opening twice the width of the other, hence x =2s and x1=s The tributary area of grav-ity loads carried by the center post as the concentrated load (P1) is as follows:
(snow+roofDL+LL) (ridge bm) (postDL)
4. Floor load to a center post be-tweeen two large marriage wall openings: Refering to the floor plan of Figure D-9I, the tributary area il-lustrated produces the concentrated gravity load (P2) to the foundation below the post as follows:
(floorLL+DL) (floor bm) (two chassis bms)
(transverse girder wt)
Note: The 2/3rds factor in the above equation is to account for an aver-age floor load situation as illustrated in Figure D-9I.
5. Total concentrated load (Rpm) to the foundation at a center post location: The roof and floor loads combine to produce the total reac-tion (Rpm) to the foundation pier or column as follows:
6. Required, adjacent opening center post location, marriage wall pier footing for Foundation Concept Type E5 and E6. The footing area (Aftg) must be large enough so that the net allowable soil bearing pres-sure (Pso) is not exceeded under the full gravity dead, live and snow loads. Note that the pier and foot-ing weight become additional dead load. The required footing area:
7. Required, adjacent opening center post location, marriage wall pier footing for Foundation Concept Type E7. The footing area (Aftg) must be large enough so that the net allowable soil bearing pressure (Pso) is not exceeded under the full grav-ity dead, live and snow loads. Note that the pier and footing weight be-come additional dead load. The re-quired footing area:
Type E5, E6 and E7 - Marriage Wall w/Two Adjacent Openings
Figure D - 9I
Note: A foundation pier or column exists, centered below the larger marriage wall opening (x = 2s) at a trans-verse girder line. The pier or column footing here should be sized only for the floor concentrated load (P2). Substitute (P2) for (Rpm) in the above two equations. This is left to the engineer and is not reflected in the Tables of Appendix B.
D-300.2 REQUIRED VERTICAL ANCHORAGE BASED ON WIND IN THE TRANSVERSE DIRECTION. Refer to Fig-ures D 10 to D 12 for the free-body diagrams of the superstructure and foundation, illustrat-ing the overturning forces due to wind and the element dead loads providing resistance. The foundation Types C, C1, E and I are included for single-section units. Figure D 4, D 5 and D 6 are also related to the equation develop-ment of this section. For allowable stress de-sign methodology, the load combination from ASCE 7 93 is: (Wind) - DL.
A. Wind Load Considerations for the Type C Single-Section Unit.
1. General: The superstructure re-ceives external and internal wind pressures or suctions (p) on the two walls and two sloping roof planes in accordance with the equation of sec-tion D 200.4.C.2. These wind pres-sures tend to overturn the super-structure, rotating it about the pivot point at the bottom of the chassis beam as shown on Figure D 10. The vertical anchorage force (Av) necessary to prevent this uplift ac-tion is located at the opposite foun-dation pier. The anchorage connec-tion of superstructure to foundation must be capable of transferring the (Av) force to the pier. The dead load of the pier, footing and soil overburden must be equal to or greater than the (Av) force to keep the superstructure from overturning.
2. Wind Loads on the Superstructure: As shown in Figure D 10, the resul-tant wind force at the top and bot-tom of the wall are (Pt) and (Pb) re-spectively. The vertical component of the resultant wind force on the windward and leeward slope are (Pvw) and (Pvl) respectively. They are calculated as follows:
3. Overturning Moment of the Super-structure: The resultant wind loads on each surface rotate about the pivot point shown in Figure D 10. The summation of the force times distance values define the equation:
4. Resisting moment of the superstruc-ture: The total dead load provides the only gravity load resistance to overturning. Using the light dead load from section D 200.1.B:
5. Required Vertical Anchorage Force: If the overturning moment (Mo) exceeds the resisting moment (Mr), an uplift force exists. The ASCE 7 93 restricts the usable dead load to 2/3rds of the actual dead load. This is the same as inverting the ratio and making the overturning moment 3/2 times the calculated value. Thus, the final equation for (Av) at a specific pier spacing is:
B. Wind Load Considerations for the Type C1 Single-Section Unit.
1. General: The same wind pressures as for Type C tend to overturn the superstructure, rotating it about the pivot point at the bottom of the chassis beam as shown on Figure D 10. The vertical anchorage force (Av) necessary to prevent this uplift action is a tie-down strap that wraps over the roof of the unit and down the side walls to anchorage below grade at concrete deadmen. The capacity of the steel straps must be capable of transferring the (Av) force to the deadman. The dead load of the concrete deadman and soil overburden must be equal to or greater than the (Av) force to keep the superstructure from overturning.
2. Wind Loads on the Superstructure: As shown in Figure D 10, the resul-tant wind forces are the same as for the Type C single-section unit. See equations in section D 300.2.A.2.
3. Overturning Moment of the Super-structure: The resultant wind loads on each surface rotate about the pivot point shown in Figure D 10. The equation is the same as for the Type C single-section unit.
4. Resisting moment of the superstruc-ture: The resisting moment is the same as for the Type C single-section unit.
5. Required Vertical Anchorage Force: The final equation for (Av) at a specific vertical tie-down strap or tie spacing is:
C. Wind Load Considerations for the Type E Single-Section Unit (excluding Types E3 and E4, which follows).
1. General: The applied wind loads to the superstructure are the same as for the Type C single-section unit. These wind pressures tend to over-turn the superstructure, rotating it about the pivot point at the exterior foundation wall as shown in Figure D 11A. The vertical anchorage force (Av) necessary to prevent this uplift action is located at the oppo-site exterior foundation wall. The anchorage connection of superstruc-ture to foundation must be capable of transferring the (Av) force to the wall. The dead load of the wall, footing and soil overburden must be equal to or greater than the (Av) force to keep the superstructure from overturning.
2. Wind Loads on the Superstructure: Same as for the Type C single-section unit. The equations are shown is section D 300.2.A2.
Wind Related Overturning Loads - Transverse Direction
Figure D - 10
3. Overturning Moment of the super-structure: The resultant wind loads on each surface rotate about the pivot point shown in Figure D 11A. The summation of the force times distance values define the equation:
4. Resisting moment of the superstruc-ture: The total dead load provides the only gravity load resistance to overturning. Using the light dead load from section D 200.1.B:
5. Required Vertical Anchorage Force: Similar to Section D 300.A.5. Thus, the final equation for anchorage force (Av) to be transferred to the exterior founda-tion wall becomes:
C-X. Wind Load Considerations for the Type E3 and E4 Single-Section Unit.
Wind Related Overturning Loads - Transverse Direction
Figure D - 11A
1. General: The applied wind loads to the superstructure are the same as for the Type C single-section unit as shown in Figure D-10. These wind pressures tend to overturn the su-perstructure, rotating it about the pivot point at the exterior founda-tion wall as shown in Figure D 11B. The vertical anchorage force (Av) necessary to prevent this uplift ac-tion is located at the two chassis beam piers and the opposite exterior foundation wall. The anchorage connection of superstructure to these piers and foundation wall must be capable of transferring the (Av) force in proportion to their distance from the pivot. The dead load of the exterior wall, footing and soil overburden; plus the dead load of the two piers, footings and soil overburden must all be equal to or greater than the portion of the (Av) force each must resist to keep the superstructure from overturning.
2. Wind Loads on the Superstructure: Same as for the Type C single-section unit. The equations are shown is section D 300.2.A2.
3. Overturning Moment of the super-structure: The resultant wind loads on each surface rotate about the pivot point shown in Figure D 11B. The summation of the force times distance values define the equation:
4. Resisting moment of the superstruc-ture: The total dead load provides the only gravity load resistance to overturning. Using the light dead load from section D 200.1.B:
5. Required vertical Anchorage Force: Assuming the anchorage force at the exterior wall to be (Av), and using triangle proportions, the intermedi-ate vertical anchorage force at the furthest pier from the pivot (Av1) becomes:
Note: As illustrated in Figure D 11B the anchorage force at the pier closest to the pivot is very small and is ignored. The anchorage force (Av1) shall be used at both piers for conservatism.
The resisting moment created by these two anchorage locations is:
Substitution of the anchorage force value (Av1) into the above equation results in the following:
Since the anchorage moment (MAV) must balance the net overturning moment (1.5 x Mo-Mr), the maxi-mum vertical anchorage force (Av), which is used in the Foundation De-sign Load Tables of Appendix B, Part 2 for the exterior wall per foot of length, becomes:
Note that the vertical anchorage force (Av1) used in the Tables for anchorage at both piers under the chassis beams is based on pier spac-ing (s) and renamed (Av1pier) in the equation becomes:
D. Wind Load Considerations for the Type I Single-Section Unit.
1. General: The applied wind loads to the superstructure are the same as for the Type C and E single-section unit. These wind pressures tend to overturn the superstructure, rotating it about the pivot point at the exte-rior foundation wall as shown in Figure D 12. The vertical anchor-age force (Av) necessary to prevent this uplift action is located at the far side chassis beam at the interior pier spacing. The anchorage connection of superstructure to foundation must be capable of transferring the (Av) force to the pier. The dead load of the wall, footing and soil overburden must be equal to or greater than the (Av) force to keep the superstruc-ture from overturning.
Wind Related Overturning Loads - Transverse Direction
Figure D - 11B
2. Wind Loads on the Superstructure: Same as for the Type C single-section unit. The equations are shown is section D 300.2.A.2.
3. Overturning Moment of the super-structure: Same as for the Type E single-section unit.
4. Resisting moment of the superstruc-ture: Same as for the Type E sin-gle-section unit.
Wind Related Overturning Loads - Transverse Direction
Figure D - 12
5. Required Vertical Anchorage Force: Similar to Section D 300.A.5. Thus, the final equation for anchorage force (Av) to be transferred to the exterior founda-tion wall becomes:
E. Wind Load Considerations for a Type C Multi-Section Unit.
1. General: The superstructure is as-sumed to behave as a single box for overturning. It receives wind loads and tends to overturn in a similar manner to the single-section unit as described in Section D 300.2.A.1. The pivot point is under the exterior chassis beam on one side. Anchor-age connection of superstructure to foundation is either two tie-downs or four tie-downs as illustrated in Figure D 13 at the other chassis beams.
2. Wind Loads on the Superstructure: As shown in Figure D 13, the resul-tant wind force at the top and bot-tom of the wall are (Pt) and (Pb) re-spectively. The vertical component of the resultant wind force on the windward and leeward slope are (Pvw) and (Pvl) respectively. They are calculated as follows:
3. Overturning Moment of the Super-structure: The summation of the force times distance values defines the equation:
4. Resisting Moment of the Super-structure: The total dead load pro-vides the only gravity load resistance to overturning. Using the light dead load for a multi-section unit from section D 200.1.B:
Mr = DL (Wt - dc)
5. Required Vertical Anchorage Force:
a. Two tie-downs:
b. Four tie-downs: by triangle proportions the intermediate vertical anchorage forces (Av) are:
The resisting moment created by the three anchorage locations is:
Substitution of the anchorage force values into the above equation results in the following:
Since the anchorage moment (MAV) must balance the net overturning moment (1.5 x Mo-Mr), the maximum vertical an-chorage force (Av) concentrated at the exterior pier, which is used in the Foundation Design Load Tables of Appendix B, Part 2, becomes:
Note that the smaller vertical anchorage forces (Av1) and (Av2) are not used in the Tables.
F. Wind Load Considerations for a Type E Multi-Section Unit.
Wind Related Overturning Loads: Type C - Multi-Section Unit - Transverse Direction
Figure D - 13
1. General: The pivot point is located at the exterior foundation wall on one side. Anchorage connection of superstructure to foundation is ac-complished at the opposite exterior wall and at specific pier locations re-sulting in either two tie-downs or four tie-downs as illustrated in Fig-ure D 14. Foundation Concept Type E3 has six tie-downs. The illustra-tion would be similar to that for four tie-downs; however, the calculations are included here.
2. Wind Loads on the Superstructure: Wind loads on the walls and roof planes are the same as for the Type C multi-section unit.
3. Overturning Moment of the Super-structure: The summation of the force times distance values defines the equation:
4. Resisting Moment of the Super-structure: The total dead load pro-vides the only gravity load resistance to overturning. Using the light dead load for a multi-section unit from section D 200.1.B:
Mr = DL Wt
5. Required Vertical Anchorage Force:
a. Two tie-downs: at the exterior wall in lbs/ft:
b. Four tie-downs: by triangle proportions the intermediate vertical anchorage forces (Av), also in lbs/ft, are:
The resisting moment created by the three anchorage locations is:
Substitution of the anchorage force values into the above equation results in the following:
Since the anchorage moment (MAV) must balance the net overturning moment (1.5 Mo-Mr), the maximum vertical an-chorage force (Av) at the exte-rior wall in lbs/ft, becomes:
And the next largest anchorage force (in lbs.) (Av1) at the first interior pier becomes:
b. Six tie-downs: by triangle pro-portions the intermediate vertical anchorage forces (Av), in lbs/ft of unit length, are:
The resisting moment created by the four anchorage locations is:
Substitution of the anchorage force values into the above re-sults in the following:
Since the anchorage moment (MAV) must balance the net overturning moment (1.5 Mo-Mr), the maximum vertical an-chorage force (Av) at the exte-rior wall in lbs/ft, becomes:
And the next largest anchorage force (in lbs.) (Av1) at the first interior pier becomes:
The smaller values of Av are not printed in the tables for fabrica-tion economy.
G. Wind Load Considerations for a Type I Multi-Section Unit.
1. General: The pivot point is located at the exterior foundation wall on one side. Anchorage connection of superstructure to foundation is ac-complished at specific pier locations resulting in either two tie-downs or four tie-downs as illustrated in Fig-ure D 15.
2. Wind Loads on the Superstructure: Wind loads on the walls and roof planes are the same as for the Type C or E unit.
3. Overturning Moment of the Super-structure: The summation of the force times distance values defines the equation: