ARE 563 SS II Class 8 – Strength Analysis Dr. Kyle Larson Today’s Class • ACI Strength Design • Quiz at End 1 Design Stress Block C a C=T d-a/2 Beam Flexural Resistance • Design flexural strength is given by fMn • For singly reinforced rectangular beams: ๐ ≤ ๐๐ 0.85๐ ๐๐ = ๐ด ๐ ๐= ๐ =๐ ๐− ๐ด ๐ 0.85๐ ๐ ๐ ๐ =๐ด ๐ ๐− 2 2 ๐= ๐ด ๐๐ ๐ = ๐๐๐๐๐๐๐๐๐๐๐๐๐ก ๐๐๐ก๐๐ 2 Strains 0.003 0.85๐ ๐๐ = ๐ด ๐ ๐= ecu ๐ด ๐ =๐ฝ๐ 0.85๐ ๐ ๐= ๐ ๐ฝ ๐ ๐−๐ = ๐ ๐ ๐ = ๐−๐ 0.003 ๐ ACI Moment Capacity d= 21” b=16” h= 24” • Determine ACI Moment Capacity ๐๐ • With f’c=5 ksi and fy=60 ksi • Max live load if L=30 feet for simplysupported As = 6 #8’s 3 ACI Moment Capacity h= 24” d= 21” b=16” As = 6 #8’s ACI Moment Capacity h= 24” d= 21” b=16” As = 6 #8’s 4 ACI Moment Capacity D= 21” B=16” H= 24” • Determine ACI Moment Capacity ๐๐ • With f’c=5 ksi and fy=60ksi • Same problem as last class period with different concrete strength • If does not work what can be done if same steel is used and architect would like to keep depth about the same As = 5 #9’s H= 24” ACI Moment Capacity D= 21” B=16” As = 5 #9’s 5 H= 24” ACI Moment Capacity D= 21” B=16” As = 5 #9’s H= 24” ACI Moment Capacity D= 21” B=16” As = 5 #9’s 6 ACI Moment Capacity D= 21” B=16” H= 24” • Determine ACI Moment Capacity ๐๐ • With f’c=4 ksi and fy=60ksi • Same problem with different concrete strength • If does not work what can be done if same steel is used and architect would like to keep depth about the same As = 5 #9’s H= 24” ACI Moment Capacity D= 21” B=16” As = 5 #9’s 7 H= 24” ACI Moment Capacity D= 21” B=16” As = 5 #9’s H= 24” ACI Moment Capacity D= 21” B=16” As = 5 #9’s 8 ACI Moment Capacity • ๐ • ∗ ∗ = = ∗ = 0.018 = ∗ h= 24” • ๐= d= 21” b=16” • Determine ACI Moment Capacity ๐๐ • With f’c=3 ksi and fy=60 ksi • If does not work what can be done if same steel is used and architect would like to keep depth about the same = 0.0027 = 0.0033 • ๐ = 0.0136 … ๐กโ๐๐ ๐ค๐๐๐ ๐๐ ๐๐ ๐๐ ๐ ๐ข๐ As = 6 #9’s ACI Moment Capacity •๐= = . ∗ ( ) . ( )( ) b=16” = 8.82“ • From ACI with f’c<4 ksi b1 = 0.85 from equation •๐ = . = 10.38“ 0.003 = . . . d= 21” = h= 24” •๐= .003 = .003 > 0.005 • We knew this As = 6 #9’s 9 ACI Moment Capacity h= 24” Increase concrete strength With 4 ksi rmax=0.0181 Increase b or d Increasing d might upset architect Let’s see what new b would have to be • 0.0136=6/(b*21) • b=21 inches • Let’s run with that • • • • • d= 21” b=16” • Options As = 6 #9’s ACI Moment Capacity h= 24” d= 21” b=21” • Determine ACI Moment Capacity ๐๐ • With f’c=3 ksi and fy=60 ksi As = 6 #9’s 10 ACI Moment Capacity h= 24” d= 21” b=21” As = 6 #9’s ACI Moment Capacity h= 24” d= 21” b=21” As = 6 #9’s 11 Questions? Please email me kyle@ksu.edu 12