Question

Homework Problem Solving TOPIC: Review of ASD and Load Resistance Factor Design A 2x6, #1 Grade, DF-L wood joists having a moisture content of 11% with a span of 13.5 ft. is shown below. The only combined load to be considered is (DL + RLL) of 34#/ft. DL-14 PSF & RLL 20 PSF with 12" O.C. Evaluate: Will the 2x6 section work for the given load? Show ASD and LRFD design method for Bending Only!! 34 13.5 Load: Wp 14 lbl ft "-=20 lb/ft Load Combination: D +L, (ASD) 1.2D+1.6L, (LRFD Span: L = 13.5 ft. Member Size: 2x6 Stress grade and Species:No.IDF-L Unbraced Length: 1" =0 Moisture Content: MC-11% Live Load Deflection limit. Allow Δ - 360

Answer 1

Use ASI Span of the floor beam 1 is 13.5 feet. The dead load plus live load Wead W The unbraced length is 0 inches 12 is 34psf x ft-34plf 12 The maximum induced moment M...is 34x13.52 774.56ft-b 774.56 x121bin.774.56psi Bending stress due to given loading is 2x63 12 Selected joist size is2x6in.. The elastic modulus of DF-L #1 grade E is 1.800.000 psi The bending strength of DF-L #1 grade Fb is 1.495 psi The value of load duration factor Cp for dead load plus live load combination is 1 (take the factor for live load with minimum duration of action) The wet service factor, CM 1s 1.0 (moisture content is 11%, which is less than 1996) The temperature adjustment factor, Cis 10 Incision factor, C.,is 1 Flat use factor, Cf,is 1.15 (for breadth of 2inches and depth of 6 inches)

Size factor, Cr is 1.3 Repetitive member factor, C, is 1.15 (for joists) The ratio of depth to width of the beam3, compute the beam stability factor Beam stability factor, Ci is 1.0. (Braced against buckling throughout the length of the beam) Calculate the adjusted bending strength. F -FCGc d 6 1,495psix1x1x1x1x1.15x1.0x1.3x1.15 2,570.28 psi>774.56psi The design is safe in bending Use LRFD Span of the floor beam 1 is 13.5 feet. The dead load plus live load 1 .2wdead + 1.6ngve Is ( 1.2 x 14 psf + 1.6 x 20 psf ) x|-|ft 12 12 48.8 plf. The unbraced length is 0 inches The maximum induced moment M...is M 48.8x13.52 ma 1,111.725ft-lb 1111.725 12lbin.111725psi Bending stress due to given loading is 2x63 12

Selected joist size is2x6in.. The elastic modulus of DF-L #1 grade E is 1.800.000 psi The bending strength of DF-L #1 grade F, is 1.495 psi The wet service factor, CM Is 1.0 (moisture content is 11%, which is less than 1996) The temperature adjustment factor, Cis 10 Incision factor, C is 1 Flat use factor, Cf,is 1.15 (for breadth of 2inches and depth of 6 inches) Size factor, Cr is 1.3 Repetitive member factor, C, is 1.15 (for joists) The ratio of depth to width of the beam--- 3>1, check the beam stability factor Beam stability factor, Ci is 1.0. (Braced against buckling throughout the length of the beam) Time effect factor, 1 is 0.7 (corresponding to live load which is of lower duration of 10 years, compared to the dead load which is permanent) Calculate the adjusted bending strength. 1,495psix1x1x1x1.15x1.0x1.3x1.15x2.54x0.85x0.7 -3,884.46psi>1,111.725psi The design is safe in bending