Solution Manual For Structural Wood Design: ASD/LRFD, 2nd Edition

Chapter 2 2-1. Solutions S2-1 Calculate the total uniformly distributed roof dead load in psf of horizontal plan area for a sloped roof with the design parameters given below. • • • • • • 2×8 rafters at 24” on centers Asphalt shingles on ½” plywood sheathing 6” insulation (fiberglass) Suspended Ceiling Roof slope: 6-in-12 Mechanical & Electrical (i.e. ducts, plumbing etc) = 5 psf Solution: 2×8 rafters at 24” on-centers = 1.2 psf Asphalt shingles (assume ¼” shingles) = 2.0 psf ½” plywood sheathing = (4 x 0.4 psf/1/8” plywood) = 1.6 psf 6” insulation (fiberglass) = 6 x 1.1 psf/in. = 6.6 psf Suspended Ceiling = 2.0 psf Mechanical & Electrical (i.e. ducts, plumbing etc) = 5.0 psf Total roof dead load, D (psf of sloped roof area) = 18.4 psf The total dead load in psf of horizontal plan area will be:  2 2 w DL = D  6 +12  , psf of horizontal plan area 12     =18.4psf (1.118) = 20.6 psf of horizontal plan area 2-2. Given the following design parameters for a sloped roof, calculate the uniform total load and the maximum shear and moment on the rafter. Calculate the horizontal thrust on the exterior wall if rafters are used. • • • • • Roof dead load, D= 20 psf (of sloped roof area) Roof snow load, S = 40 psf (of horizontal plan area) Horizontal projected length of rafter, L2 =14 ft Roof slope: 4-in-12 Rafter or Truss spacing = 4’ 0 Solutions:  2 2 Sloped length of rafter, L1 =  4 +12  (14 ft ) =14.8 ft 12     Chapter 2 Solutions S2-2 Using the load combinations in section 2.1, the total load in psf of horizontal plan area will be: L  wTL = D  1  + (Lr or S or R), psf of horizontal plan area L   2   = 20 psf  14.8′  + 40 psf  14′  = 61.1 psf of horizontal plan area The total load in pounds per horizontal linear foot (Ib/ft) is given as, wTL (Ib/ft) = wTL (psf) x Tributary width (TW) or Spacing of rafters = 61.1 psf (4 ft) = 244.4 lb/ft. h = (4/12) (14 ft) = 4.67 ft The horizontal thrust H is, H=  L2    244.4 Ib/ft 14′  14′   2 2  =   wTL ( L2 )  h ( ) 4.67′ = 5129 Ib. The collar or ceiling ties must be designed to resist this horizontal thrust. L2 = 14’ The maximum shear force in the rafter is, L    Vmax = wTL  2  = 244.4  14′  = 1711 Ib  2   2    The maximum moment in the rafter is, w (L ) M max = TL 2 8 2-3. 2 244.4 (14′ ) = = 5989 ft-Ib = 5.9 ft-kip 8 2 Determine the tributary widths and tributary areas of the joists, beams, girders and columns in the panelized roof framing plan shown below. Assuming a roof dead load of 20 psf and an essentially flat roof with a roof slope of ¼” per foot for drainage, determine the following loads using the IBC load combinations. Neglect the rain load, R and assume the snow load, S is zero: a. b. c. d. The uniform total load on the typical roof joist in Ib/ft The uniform total load on the typical roof girder in Ib/ft The total axial load on the typical interior column, in Ib. The total axial load on the typical perimeter column, in Ib Chapter 2 Solutions S2-3 . Solution: The solution is presented in a tabular format as shown below: Tributary Widths and Tributary Areas of Joists, Beams and Columns Structural Member Purlin Glulam girder Typical interior Column Typical perimeter Column Tributary Width (TW) 10′ + 10′ =10′ 2 2 20′ + 20′ = 20′ 2 2 Tributary Area (TA) 10’ x 20’ = 200 ft 2 20’ x 60’ = 1200 ft 2  20′ 20′   60′ 60′   2 + 2   2 + 2  =     20′ 20′   60′  + =  2   2   2 1200 ft 600 ft 2 Since the snow and rain load are both zero, the roof live load, Lr will be critical. With a roof slope of ¼” per foot, the number of inches of rise per foot, F = ¼ = 0.25 Purlin: The tributary width TW = 10 ft and the tributary area, TA = 200 ft2 600, and from section 2.4, we obtain: R1 = 0.6, and R2 = 1.0 Using equation 2-4 gives the roof live load, Lr = 20 x 0.6 x 1 = 12 psf The total loads are calculated as follows: wTL (psf) = (D + Lr) = 20 + 12 = 32 psf wTL (Ib/ft) = wTL (psf) x tributary width (TW) = 32 psf x 20 ft = 640 Ib/ft Typical Interior Column: 2 Chapter 2 Solutions The tributary tributary area of the typical interior column, TA = 1200 ft Thus, TA > 600, and from section 2.4, we obtain: S2-4 2 R1 = 0.6, and R2 = 1.0 Using equation 2-4 gives the roof live load, Lr = 20 x 0.6 x 1 = 12 psf The total loads are calculated as follows: wTL (psf) = (D + Lr) = 20 + 12 = 32 psf 2 The Column Axial Load, P = 32 psf x 1200 ft = 38, 400 Ib = 38.4 kips Typical Perimeter Column: 2 The tributary tributary area of the typical perimeter column, TA = 600 ft Thus, from section 2.5.1, we obtain: R1 = 0.6, and R2 = 1.0 Using equation 2-4 gives the roof live load, Lr = 20 x 0.6 x 1 = 12 psf The total loads are calculated as follows: wTL (psf) = (D + Lr) = 20 + 12 = 32 psf 2 The Column Axial Load, P = 32 psf x 600 ft = 19, 200 Ib = 19.2 kips 2-4. A building has sloped roof rafters (5:12 slope) spaced at 2’ 0” on centers and is located in Hartford, Connecticut. The roof dead load is 22 psf of sloped area. Assume a fully exposed roof with terrain category “C”, and use the ground snow load from the IBC or ASCE 7 snow map (a) Calculate the total uniform load in lb/ft on a horizontal plane using the IBC. (b) Calculate the maximum shear and moment in the roof rafter. Solution: The roof slope,  for this building is 22.6, Roof Live Load, Lr: From Section 2.4, the roof slope factor is obtained as, F=5  R2 = 1.2 – 0.05 (5) = 0.95 Assume the tributary area (TA) of the rafter < 200 ft2, The roof live load will be, Lr = 20R1R2 = 20(1.0)(0.95) = 19 psf  R1 = 1.0 Chapter 2 Solutions Snow Load: Using IBC Figure 1608.2 or ASCE 7 Figure 7-1, the ground snow load, Pg for Hartford, Connecticut is 30 psf. Assuming a building with a warm roof and fully exposed, and a building site with terrain category “C”, we obtain the coefficients as follows: Exposure coefficient, Ce = 0.9 (ASCE 7 Table 7-2) The thermal factor, Ct = 1.0 (ASCE 7 Table 7-3) The Importance Factor, I = 1.0 ASCE Table 7-4 The slope factor, Cs = 1.0 (ASCE Figure 7-2 with roof slope,  = 22.6 and a warm roof) The flat roof snow load, Pf = 0.7 Ce Ct I Pg = 0.7 x 0.9 x 1.0 x 1.0 x 30 = 18.9 psf Minimum flat roof snow load, Pm = 20Is = 20 (1.0) = 20 psf (governs) Thus, the design roof snow load, Ps = Cs Pf = 1.0 x 20 = 20 psf Therefore, the snow load, S = 20 psf The total load in psf of horizontal plan area is given as, L  wTL = D  1  + (Lr or S or R) , psf of horizontal plan area L   2 Since the roof live load, Lr (18 psf) is smaller that the snow load, S (20 psf), the snow load is more critical and will be used in calculating the total roof load.  2 2 wTL = 22 psf  5 +12  + 20 psf 12    =  43.83 psf of horizontal plan area The total load in pounds per horizontal linear foot (Ib/ft) is given as, wTL (Ib/ft) = wTL (psf) x Tributary width (TW) or Spacing of rafters = 43.83 psf (2 ft) = 87.7 lb/ft. Assume L2 = 14’ The maximum moment in the rafter is, 2 2 87.7 (14') wTL ( L2 ) M max = = = 2149 ft-Ib = 2.15 ft-kip 8 8 S2-5 Chapter 2 2-5. Solutions S2-6 A 3-story building has columns spaced at 18 ft in both orthogonal directions, and is subjected to the roof and floor loads shown below. Using a column load summation table, calculate the cumulative axial loads on a typical interior column with and without live load reduction. Assume a roof slope of ¼” per foot for drainage. Roof Loads: Dead Load, Droof = 20 psf Snow Load, S = 40 psf 2nd and 3rd Floor Loads: Dead Load, Dfloor = 40 psf Floor Live Load, L = 50 psf Solution: At each level, the tributary area (TA) supported by a typical interior column is 18’ x 18’ = 324 ft2 Roof Live Load, Lr: From section 2.4, the roof slope factor is obtained as, F = ¼ = 0.25  R2 = 1.0 Since the tributary area (TA) of the column = 324 ft2,  R1 = 1.2 – 0.001 (324) = 0.88 The roof live load will be, Lr = 20R1R2 = 20(0.88)(1.0) = 17.6 psf 400 ft2  Live Load reduction allowed 4 50 psf KLL AT = 2592 > 400 ft2  Live Load reduction allowed 0.25 + 15/(4 x 648) = 0.54 40 psf (Snow load) 0.67 x 50 = 33.5 psf ≥ 0.50 Lo = 25 psf 0.54 x 50 = 27 psf ≥ 0.40 Lo = 20 psf The column axial loads with and without floor live load reduction are calculated using the column load summation tables below: Chapter 2 Solutions S2-8 Column Load Summation Table Design Live Load Level Tributar y area, (TA) Dead Load, D (ft2 ) (psf) Live Load, Lo (S or Lr or R on the roof) Roof: S or Lr or R Floor: L Roof: D Floor: D + L Roof: D+0.75S Floor: D+0.75L Unfactore d Column Axial Load at each level, P= (TA)(ws1) or (TA)(ws2) (psf) (psf) (kips) Unfactored total load at each level, ws1 Unfactored total load at each level,ws2 (psf) (psf) Cumulative Unfactored Axial Load, PD+L (kips) Maximum Cumulative Cumulative Unfactored Unfactored Axial Axial Load, Load, P PD+0.75L+0. 75S (kips) (kips) Roof 3rd Flr 324 324 20 40 40 50 40 33.5 2nd Flr 324 40 50 27 Roof Third floor Secon d floor 324 324 20 40 40 50 40 50 324 40 50 50 With Floor Live Load Reduction 20 50 6.5 or 16.2 73.5 65.1 23.8 or 21.1 67 60.3 21.7 or 19.5 Without Floor Live Load Reduction 20 50 6.5 or 16.2 90 77.5 29.2 or 25.1 90 77.5 29.2 or 25.1 6.5 30.3 16.2 37.3 16.2 37.3 52 56.8 56.8 6.5 35.7 16.2 41.3 16.2 41.3 64.9 66.4 66.4 Chapter 2 2-6. Solutions S2-9 A 2-story wood framed structure 36 ft x 75 ft in plan is shown below with the following given information. The floor to floor height is 10 ft and the truss bearing (or roof datum) elevation is at 20 ft and the truss ridge is 28 ft 4” above the ground floor level. The building is “enclosed” and located in Rochester, New York on a site with a category “C” exposure. Assuming the following additional design parameters, calculate: Floor Dead Load = Roof Dead Load = Exterior Walls = Snow Load (Pf) = 30 psf 20 psf 10 psf 40 psf Site Class = Importance (Ie)= SS = S1 = R= D 1.0 0.25% 0.07% 6.5 (a) The total horizontal wind force on the main wind force resisting system (MWFRS) in both the transverse and longitudinal directions. (b) The gross vertical wind uplift pressures and the net vertical wind uplift pressures on the roof (MWFRS) in both the transverse and longitudinal directions. (c) The seismic base shear, V, in kips (d) The lateral seismic load at each level in kips Solution: (a) Lateral Wind Roof Slope: Run = 18’, Rise = 8’-4”,  = 25 Assuming a Category II building V = 115mph (ASCE 7 Table 26.5-1A) Wind Pressures (from ASCE 7, Figure 28.6-1): Transverse ( = 25): Horizontal Zone A: 26.3 psf Zone B: 4.2 psf Zone C: 19.1 psf Zone D: 4.3 psf Vertical Zone E: -11.7 psf Zone F: -15.9 psf Zone G: -8.5 psf Zone H: -12.8 psf Chapter 2 Solutions S2-10 Longitudinal: ( = 0): Horizontal Zone A: 21 psf Zone B: N/A Zone C: 13.9 psf Zone D: N/A Vertical Zone E: -25.2 psf Zone F: -14.3 psf Zone G: -17.5 psf Zone H: -11.1 psf End Zone width: a:  0.1 x least horizontal dimension of building  0.4 x mean roof height of the building and  0.04 x least horizontal dimension of building  3 feet a  0.1 (36’) = 3.6’ (governs)  20’+28.33′   (0.4)  = 9.67’ 2    0.04 (36’) = 1.44’  3 feet Therefore the Edge Zone = 2a = 2 (3.6’) = 7.2’ Average horizontal pressures: Transverse:  (end zone )(end zone pressure ) + (bldg width − end zone )(int erior zone pressure )   q avg =  (bldg width )    (7.2′)(26.3 psf ) + (75’− 7.2′)(19.1 psf )  qavg ( wall ) =   = 19.8 psf (Zones A, C) (75′)    (7.2′)(4.2 psf ) + (75’− 7.2′)(4.3 psf )  qavg (roof ) =   = 4.3 psf (Zones B, D) (75′)   Chapter 2 Solutions Longitudinal:  (7.2′)(21 psf ) + (36’− 7.2′)(13.9 psf )  qavg ( wall ) =   = 15.32 psf (Zones A, C) (36′)   Design wind pressures: Height and exposure coefficient:  20’+28.33′  Mean roof height =   = 24.2’ 2    = 1.35 (ASCE 7 Figure 28.6-1, Exposure = C, h  25’) Transverse wind: P = qavg Pwall = (19.8 psf)(1.35) = 26.73 psf Proof = (4.3 psf)(1.35) = 5.81 psf Longitudinal wind: Pwall = (15.32 psf)(1.35) = 20.7 psf Total Wind Force: Transverse wind: PT = (26.73 psf )(10’+ 10′) + (5.81 psf )(8.33′) (75′) = 43.7 kips (base shear, transverse) Longitudinal wind: 8.33′   PT =  20 ‘+  (20.7 psf )(36 ‘) = 18.0 kips (base shear, longitudinal) 2   S2-11 Chapter 2 Solutions S2-12 (b) Wind Uplift Average vertical pressures: P = qavg From Part (a), base uplift pressures: Transverse: Zone E: -11.7 psf Zone F: -15.9 psf Zone G: -8.5 psf Zone H: -12.8 psf Longitudinal: Zone E: -25.2 psf Zone F: -14.3 psf Zone G: -17.5 psf Zone H: -11.1 psf Transverse:   36′   36′   Pu ,avg = (−11.7 psf − 15.9 psf )(7.2′)   + (−8.5 psf − 12.8 psf )(75’− 7.2′)    (1.35)  2   2   = – 39,922 lb. qu ,avg = −39,922 lb = – 14.8 psf (gross uplift, transverse) (75’)(36 ‘) Longitudinal:   75′   75′   Pu ,avg = (−25.2 psf − 14.3 psf )(7.2′)   + (−17.5 psf − 11.1 psf )(36’− 7.2′)    (1.35)  2   2   = – 56,097 lb. qu ,avg = −56, 097 lb = – 20.8 psf (gross uplift, longitudinal) (75’)(36 ‘) Net factored uplift (Longitudinal controls): qnet = 0.9D+W =(0.9)(20psf) + (-20.8psf) = -2.8psf (net uplift) Chapter 2 Solutions S2-13 (c) Seismic base shear Calculate “W” for each level Level Area (ft.2) Roof 75’ x 36’ = 2700 ft.2 Trib. Height (ft.) Wt. Level (kip)* Wt. Walls (kip) Wtotal (kip) (10’/2)= 5’ (2700 ft2) x [20psf + (0.2x40psf)] = 75.6k (5’) x (10psf) x (2) x (75’ + 36’) = 11.1k 75.6k + 11.1k = 86.7k (10’) x (10psf) x 81.0k + 2 (2) x (75’ + 36’) = 22.2k = 22.2k 103.2k W = 86.7k + 103.2k = 189.9k * Note: Where the flat roof snow load, Pf, is greater than 30psf, then 20% of the flat roof snow load shall be included in “W” for the roof (ASCE 7 Section 12.14.8.1 ) nd 75’ x 36’ = 2700 ft.2 (10’/2) + (10’/2) = 10’ (2700 ft2) x (30psf) = 81.0k Seismic Variables: Fa = Fv = 1.6 (ASCE 7 Table 11.4-1) 2.4 (ASCE 7 Table 11.4-2) ) SMS = Fa SS = (1.6) ( 0.25) = 0.40 SM1 = Fa S1 = (2.4) ( 0.07) = 0.168 SDS = (2/3) SMS = (2/3) ( 0.40) = 0.267 SD1 = (2/3) SM1 = (2/3) ( 0.168) = 0.112 Base Shear: V= F SDS W R V= (1.1) (0.267) (189.9) = 8.58k (6.5) Chapter 2 Solutions (d) Seismic Forces at each level: …. Fx = F SDS Wx R FR = (1.1) (0.267) (86.7) = 3.92k (6.5) F2 = (1.1) (0.267) (103.2) = 4.67k (6.5) S2-14 Chapter 2 Solutions 2-7 (see framing plan and floor section) a) Determine the floor dead load in PSF b) Determine the service dead and live loads to J-1 and G-1 in PLF c) Determine the maximum factored loads in PLF to J-1 and G-1 d) Determine the factored maximum moment and shear in J-1 and G-1 e) Determine the maximum service and factored load in kips to C-1 S2-15 Chapter 2 Solutions S2-16 Chapter 2 Solutions S2-17 Chapter 2 2-9. w = 500plf; L1 = 20ft Case 1: continuous over support Solutions S2-18 Chapter 2 Solutions Case 2: hinged over support Case 1 would have less deflection Case 2 is easier to build; 40ft section might be hard to get or ship/handle on-site S2-19 Chapter 2 2-10 Solutions S2-20 Chapter 2 Solutions a) List each truss member in a table (B1, B2, T1, T2, W1 to W6) and list the following: size, length, species, grade, density, weight). b) Calculate the total weight of the truss using the table in (a). S2-21 Chapter 2 Solutions S2-22 Chapter 2 Solutions S2-23 c) Draw a free-body diagram of the truss and indicate the uniformly distributed loads to the top and bottom chords in pounds per lineal foot (plf) and indicate the supports. d) Calculate the maximum possible reaction using the controlling load case Dead + Snow. Trib width = 2 ft. Top chord: wD = (2)(10) = 20plf wLr = (2)(20) = 40plf wS = (2)(30.8) = 61.6plf Bot. chord: wD = (2)(10) = 20plf wD = 20+20 = 40 plf wS = 61.6 plf Rmax = ( 20 + 20 + 61.6)(19.41) =986 lb. 2 d) What are the maximum compression loads to W2, W5, and W6 and what is the purpose of the single row of bracing at midpoint? W2 – 860 lb W5 – 899lb W6 – 354 lb The bracing limits the unbraced length of the members being braced and prevents buckling under compression. Chapter 2 2-11: Given Loads: Uniform load, w D = 500plf L = 800plf S = 600plf Beam length = 25 ft. Solutions S2-24 Concentrated Load, P D = 11k S = 15k W = +12k or -12k E = +8k or – 8k Do the following: a) Describe a practical framing scenario where these loads could all occur as shown. b) Determine the maximum moment for each individual load effect (D, L, S, W, E) c) Develop a spreadsheet to determine the worst-case bending moments for the code-required load combinations. Chapter 2 Solutions a) Transfer beam that has loads transferred from the roof down to a floor level. S2-25 Chapter 2 Solutions S2-26 Load Combinations Uniform Loads Concentrated Loads wD = 500plf wL = 800plf PD = 11kips PS = 15kips wS = 600plf PW = 12kips PE = 8kips LB = 25ft PWup = −12kips PEup = −8kips 2 wDLB PDLB MD = + = 108 ft kips 8 4 MW = PWLB = 75 ft kips 4 MWup = PWupLB = −75 ft kips 4 ME = PELB = 50 ft kips 4 MEup = PEupLB = −50 ft kips 4 2 wLLB ML = = 62 ft kips 8 2 wS LB PS LB MS = + = 141 ft kips 8 4 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( LC1 = 1.4 MD = 151 ft kips LC2 = 1.2 MD + 1.6 ML + 0.5 MS = 300 ft kips LC3a = 1.2 MD + 1ML + 1.6 MS = 417 ft kips ) LC3b = 1.2 MD + 0.5 MW + 1.6 MS = 392 ft kips ( ) ( ) ( ) ( ) LC5 = ( 1.2 MD) + ( ME) + ( ML) + ( 0.2 MS) = 270 ft kips LC4 = 1.2 MD + 1.6 MW + ML + 0.5 MS = 382 ft kips ( ) ( ( ) ( ) LC6 = 0.9 MD + 1.0 MWup = 22ft kips ) LC7 = 0.9 MD + MEup = 47ft kips Mmax = max(LC1  LC2  LC3a  LC3b  LC4  LC5) = 417 ft kips MmaxUp = min(LC6  LC7) = 22ft kips Chapter 2 Solutions S2-27 2-12 (see framing plan) Assuming a roof dead load of 25 psf and a 25 degree roof slope, determine the following using the IBC factored load combinations. Neglect the rain load, R and assume the snow load, S is zero: e. Determine the tributary areas of B1, G1, C1, and W1 f. The uniform dead and roof live load and the factored loads on B1 in PLF g. The uniform dead and roof live load on G1 and the factored loads in PLF (Assume G1 is uniformly loaded) h. The total factored axial load on column C1, in kips i. The total factored uniform load on W1 in PLF (assume trib. length of 50 ft.) Chapter 2 Solutions S2-28 Chapter 2 Solutions S2-29 Chapter 2 Solutions S2-30 2-13. A 3-story building has columns spaced at 25 ft in both orthogonal directions, and is subjected to the roof and floor loads shown below. Using a column load summation table, calculate the cumulative axial loads on a typical interior column. Develop this table using a spreadsheet. Submit a hard copy that is properly formatted with your HW and submit the XLS file by e-mail. Roof Loads: 2nd & 3rd floor loads Dead, D = 20psf Dead, D = 60psf Snow, S = 45psf Live, L = 100psf All other loads are 0 Chapter 2 Solutions S2-31 2-14 Using only the loads shown and the weight of the concrete footing only (conc = 150pcf), determine the required square footing size, BxB using the appropriate load combination to keep the footing from overturning about point A (i.e. – either load combination 6 or 15 Chapter 2 of the text). Loads shown are service level (Mw = 0.6W = 45k-ft) PD = 10kips B = 7.67ft MW = 45ft kips  conc = 150pcf Pftg = BBH conc = 11.8 kips H = 1.333ft Overturning Moment Resisting Moment OM = MW = 45ft kips B RM = PD + Pftg  = 83.5 ft kips 2 ( ASD Load Comb UnityASD = ( 0.6 RM) OM ) LRFD Load Comb = 1.113 Use B=7.28ft for ASD and 7.67ft for LRFD UnityLRFD = ( 0.9 RM) = 1.002  OM     0.6  must be greater than 1.0 Chapter 2 Solutions 2-15. Given: Location – Massena, NY; elevation is less than 1000 feet Total roof DL = 25psf Ignore roof live load; consider load combination 1.2D+1.6S only Use normal occupancy, temperature, and exposure conditions Length of B-1, B-2 is 30 ft. Find: a) Flat roof snow load and sloped roof snow load b) Sliding snow load c) Determine the depth of the balanced snow load and the sliding snow load on B-1 and B-2 d) Draw a free-body diagram of B-1 showing the service dead and snow loads in PLF e) Find the factored Moment and Shear in B-1. S2-32 Chapter 2 Solutions S2-33 Chapter 2 Solutions S2-34 2-16. Given: Location – Pottersville, NY; elevation is 1500 feet Total roof DL = 20psf Ignore roof live load; consider load combination 1.2D+1.6S only Use normal occupancy, temperature, and exposure conditions Find: a) Flat roof snow load b) Depth and width of the leeward drift and windward drifts; which one controls the design of J1? c) Determine the depth of the balanced snow load and controlling drift snow load d) Draw a free-body diagram of J-1 showing the service dead and snow loads in PLF Chapter 2 Solutions S2-35 Chapter 2 Solutions Problem 2-16 Part (e) Factored Reactions and Maximum Moment: RA = 63.18 kips RB = 46.85 kips Mu, max = 1207.6 ft-kips (occurs at 51.55 ft from B) S2-36