Consider the framing plan drawn below. Wood joists span from Gridline A to B and B...

 

    

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Consider the framing plan drawn below. Wood joists span from Gridline A to B and B to C. Beams support the joints along Gridlines A, B, and C. There are columns at Gridlines A1, A2, A3, B1, B2, B3, C1, C2. Loads on the structure are as follows: Self-weight = 10 psf Dead load = 15 psf Live Load = 40 psf 1 2 3 A 12¹-6" Beam 1a -..0-.0L A2 10'-0"- B Beam 1b -8'-0"- B2 2x10 WOOD JOISTS SPACED AT 30" ON CENTER WOOD COLUMN, TYPICAL WOOD BEAM, TYPICAL PLYWOOD DECK (SPANS UP/DOWN ON PAGE) Based on the drawing and the information given above, determine the following: a. Calculate the total uniform load w j (in Ksi units.) b. based on their tributary areas, calculate the total load (in lbs) on the following columns: Column A2: Column B2: c. Calculate the required cross-sectional area Areq of column B2 with a safety factor of 3 and assuming an allowable axial stress of wood ow= 1500psi. Identify dimensions b x d for a square cross-section, rounding to the nearest whole-inch. Represent your answer with a dimensioned diagram. d. Based on your previous answer, Calculate the critical buckling load, Per of column B2, assuming Etimber = 1,600 ksi. Does your column fail by crushing or buckling? e. Calculate the uniform total load (in plf units) on the following beams: Beam 1a: Beam 1b: f. Calculate the maximum bending moment Mmax (in kip-inch units) in one of the simply supported joists between gridline A and B. Hint: you'll need to use the wj value you found in question (a) and an equation from the table below. SIMPLE BEAM-UNIFORMLY DISTRIBUTED LOAD Total Equiv. Uniform Load R=V .. R M max. И 1/24 Shear wl +² 2 Moment R I Vx . . M max. (at center) Mx Amax. (at center Ax ... r) .. ... =wl wl - 201 - w ( 1/12 - x) 16 w12 8 = 10x (1-x) 5 w14 384 El WX 24EI (13-21x2+x³) g. Calculate the maximum internal bending stress ob in the joist. You may assume the actual dimensions of the joist are 2" x 10". If the maximum allowable bending stress for this wood species is 1000 psi, can the 2" x 10" wood member support the load? Explain using complete sentences and using your calculations as evidence. h. Calculate the Allowable deflection Aallow of the joist using L/300. Your answer should be in units of inches. 1. Using the equation for max deflection Amax of a joist/beam with a uniformly load, calculate the required moment of inertia Ireq. Assume E = 1,400,000 psi. Is the 2" x 10" joist adequate for deflections? Explain using complete sentences and using your calculations as evidence. Consider the framing plan drawn below. Wood joists span from Gridline A to B and B to C. Beams support the joints along Gridlines A, B, and C. There are columns at Gridlines A1, A2, A3, B1, B2, B3, C1, C2. Loads on the structure are as follows: Self-weight = 10 psf Dead load = 15 psf Live Load = 40 psf 1 2 3 A 12¹-6" Beam 1a -..0-.0L A2 10'-0"- B Beam 1b -8'-0"- B2 2x10 WOOD JOISTS SPACED AT 30" ON CENTER WOOD COLUMN, TYPICAL WOOD BEAM, TYPICAL PLYWOOD DECK (SPANS UP/DOWN ON PAGE) Based on the drawing and the information given above, determine the following: a. Calculate the total uniform load w j (in Ksi units.) b. based on their tributary areas, calculate the total load (in lbs) on the following columns: Column A2: Column B2: c. Calculate the required cross-sectional area Areq of column B2 with a safety factor of 3 and assuming an allowable axial stress of wood ow= 1500psi. Identify dimensions b x d for a square cross-section, rounding to the nearest whole-inch. Represent your answer with a dimensioned diagram. d. Based on your previous answer, Calculate the critical buckling load, Per of column B2, assuming Etimber = 1,600 ksi. Does your column fail by crushing or buckling? e. Calculate the uniform total load (in plf units) on the following beams: Beam 1a: Beam 1b: f. Calculate the maximum bending moment Mmax (in kip-inch units) in one of the simply supported joists between gridline A and B. Hint: you'll need to use the wj value you found in question (a) and an equation from the table below. SIMPLE BEAM-UNIFORMLY DISTRIBUTED LOAD Total Equiv. Uniform Load R=V .. R M max. И 1/24 Shear wl +² 2 Moment R I Vx . . M max. (at center) Mx Amax. (at center Ax ... r) .. ... =wl wl - 201 - w ( 1/12 - x) 16 w12 8 = 10x (1-x) 5 w14 384 El WX 24EI (13-21x2+x³) g. Calculate the maximum internal bending stress ob in the joist. You may assume the actual dimensions of the joist are 2" x 10". If the maximum allowable bending stress for this wood species is 1000 psi, can the 2" x 10" wood member support the load? Explain using complete sentences and using your calculations as evidence. h. Calculate the Allowable deflection Aallow of the joist using L/300. Your answer should be in units of inches. 1. Using the equation for max deflection Amax of a joist/beam with a uniformly load, calculate the required moment of inertia Ireq. Assume E = 1,400,000 psi. Is the 2" x 10" joist adequate for deflections? Explain using complete sentences and using your calculations as evidence.