CIE 306 Notes Rectangular Beams, Fall 2012

CIE 306 CONCRETE STRUCTURES I A- Procedure for the analysis of Rectangular Singly-Reinforced Beams a. Assume tension steel yields y s  f  f b. Calculate the depth of the stress block b f A f a c y s .0 85 '  c. Determine the depth of the neutral axis 1 c  a d. Check the strain in the tension steel using similar triangles c c d s   .0 003  i. If 9.0 .0 005        f and f Beam is tension controlled y s s ii. If 3 ) 250 ( .0 65 .0 005 .0 002 y t y s s and f f beam is in transition             iii. If s s s s s c c s c s s c s s y s s E Calculate f c c d Calculate c Calculate A Ed A Ec bc f bc f c c d A E cb f A E f ab f A C T f and f is compression controlled Beam                              003 .0 0 .0 003 .0 003 85 .0 .0 85 .0 003 .0 85 85 .0 .0 65 002 .0 2 1 ' 1 ' 1 ' ' e. Determine c where a a d A f M s s n 1 2             B- Procedure for the Design of Rectangular Singly-Reinforced Beams (Restricted Design) a. Calculate U = 1.2 WDL+1.6 WLL b. Calculate Mu from U c. φMn=Mu d. bd k M n 2    e. Assume tension controlled beam 9.0    f. Assume  h  3 d g. Calculate bd 2 M k n    h. Calculate     .0 59 ' 1   cf by solving k i. Calculate y c f   f ' Caesar Abi Shdid, Ph.D., P.E. 1 j. Check .0 005 1 .0 85 .0 003 ' 1          y c s f f    k. Calculate bd As   l. Check         b d f b d f f where A A A w y w y c s s s 200 3 ' min min m. Select steel from Table A-2 and check if it fits within b from Table A-3. n. Check assumed actual d d  C- Procedure for the Design of Rectangular Singly-Reinforced Beams (Free Design) a. Calculate U’ = 1.2 WDL+1.6 WLL b. Calculate Mu from U’ c. φMn=Mu d. bd k M n 2    e. Assume .0 0075 s  f. Calculate         1 .0 85 .0 003 1 ' y c s f f from the equation     g. Calculate ' c y f   f h. Calculate    .0 59 ' 1   cf k i. Assume   3 2 4 2 2 2 k M b k b b M b d b d u u          j. Calculate 3 2    d b and h d k. Determine weight of beam as .0 15 144 bh wb   l. Calculate U = U’ +1.2 wb m. Calculate new Mu from U n. Calculate bd 2 M k u   o. Calculate     .0 59 ' 1   cf by solving k p. Calculate y c f   f ' q. Check .0 005 1 .0 85 .0 003 ' 1          y c s f f    r. Calculate bd As   Caesar Abi Shdid, Ph.D., P.E. 2 s. Check         b d f b d f f where A A A w y w y c s s s 200 3 ' min min t. Select steel from Table A-2 and check if it fits within b from Table A-3. Caesar Abi Shdid, Ph.D., P.E. 3