# Calculating the stiffness factors k for each span

• gichiapaul
• 130

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// calculating the STIFFNESS FACTORS (K) for each span // depends on support conditions if (leftspt == "pinned") { kab = 0.75*(iab/sab); } else if (leftspt == "fixed") { kab = (iab/sab); // note the reduction to 0.75 when an end support is pinned // remains I/L when fixed we are now calculating the stiffness factors (K) as K = I/L. as is mentioned in the // comments, a reduction of ¾ in the stiffness value occurs if an end support is pinned. } kbc = (ibc/sbc); if (rightspt == "pinned") { kcd = 0.75*(ibc/sbc); } else if (rightspt == "fixed") { kcd = (ibc/sbc); } // summing the stiffnesses at the supports B and C sumkb = kab+kbc; sumkc = kbc+kcd; the stiffness values of the spans meeting at one support are summed to enable the distribution factors (next step) to be calculated // now to calculate the DISTRIBUTION FACTORS for each end if (leftspt == "pinned") { dfab = 0; } else if (leftspt == "fixed") { dfab = 1; // basic condition of (1) if fixed // no distribution mmts (0) to a pinned support } rule of thumb: no moments can be distributed to a pinned support and the DF at a fixed end is always 1. dfba = kab/sumkb; Fady R. S. Rostom Fadzter Media Page-100
FADZTER Engineering Computer Analysis & Reinforced Concrete Design of Beams dfbc = kbc/sumkb; dfcb = kbc/sumkc; dfcd = kcd/sumkc; continuation of calculating the Distribution Factors. The actual equation is: BC AB B AB AB K K K K DF if (rightspt == "pinned") { dfdc = 0; } else if (rightspt == "fixed") { dfdc = 1; // basic condition of (1) if fixed // no distribution mmts (0) to a pinned support } the moment distribution iterations begin here: // 1st ITERATION // now calculating DISTRIBUTION MOMENTS dmab01 = 0; dmba01 = -(femba+fembc)*dfba; dmbc01 = -(femba+fembc)*dfbc; dmcb01 = -(femcb+femcd)*dfcb; dmcd01 = -(femcb+femcd)*dfcd; dmdc01 = 0; the distribution moments can be calculated as minus the sum of the fixed end moments meeting at one support multiplied by the directional distribution factor. // and now for the CARRY OVER MOMENTS //(can only carry over to a Fixed Suport) if (leftspt == "pinned") { comab01 = 0; femab = 0; } else if (leftspt == "fixed") { comab01 = 0.5*dmba01; } comba01 = 0; combc01 = 0.5*dmcb01; comcb01 = 0.5*dmbc01; comcd01 = 0; if (rightspt == "pinned") { comdc01 = 0; femdc = 0; } else if (rightspt == "fixed") { comdc01 = 0.5*dmcd01; } Fady R. S. Rostom Fadzter Media Page-101
FADZTER Engineering Computer Analysis & Reinforced Concrete Design of Beams the previous section calculates the carry over moments in the first iteration. If a support is pinned, no moments can be carried over to it. Otherwise, if fixed, a half of the distributed moment (with the same sign) is carried over to the net support. note the last line that sets the FEM to zero if pinned, this is to avoid a situation where the user intentionally sets a Fixed End Moment, other than zero. This line ensures that the FEM value does not find its way into the summation as a final moment at a pinned end. // 2nd ITERATION dmab02 = 0; dmba02 = -(comba01+combc01)*dfba; dmbc02 = -(comba01+combc01)*dfbc; dmcb02 = -(comcb01+comcd01)*dfcb; dmcd02 = -(comcb01+comcd01)*dfcd; dmdc02 = 0; if (leftspt == "pinned") { comab02 = 0; } else if (leftspt == "fixed") { comab02 = 0.5*dmba02; } comba02 = 0; combc02 = 0.5*dmcb02; comcb02 = 0.5*dmbc02; comcd02 = 0; if (rightspt == "pinned") { comdc02 = 0; } else if (rightspt == "fixed") { comdc02 = 0.5*dmcd02; }

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• Spring '16
• English, Moment distribution method, fady r. s., r. s. rostom

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