CE Calculators > Absolute Maximum B.M. in simple beam > due to 3 moving loads

Absolute Maximum moment in a simple beam due to 3 moving loads

Absolute Maximum moment due to 3 moving loads

This calculator is to determine absolute maximum bending moment (BM) in a simply supported beam with span L due to 3 moving loads (P1, P2, P3). We know that maximum BM under a moving load occures when this load and the resultant (centroid) of the load system are placed equidistant from the beam center. Initially the calculator determines the position of resultant (FR) i.e. centroid with reference to the leading load P1. It also determines the position of centroid with reference to all the loads. If the distance of a load from the centroid is +ve, it is on the right of the centroid whereas if this distance is negative that load is on the left of the resultant. The concept of influence line diagram (ILD) is used to determine values of BM. This calculator uses trial and error method to determine the maximum BM under each load and finally the maximum of all the trials is taken as the absolute maximum bending moment. It also tells under which load the absolute maximum BM occures and what is its location from support A.

By default this calculator is using the units of load as 'kN', distance as 'm' and BM as 'kNm'. Other units like kip for load, ft for distance and ft-kip for BM can also be used to get the result in the relevant units without affecting the calculated values.

Please refer to the figure and enter the required values in the form given below and then click "Calculate".

INPUT VALUES
Distance L (m):
Distance L1 (m):
Distance L2 (m):

all the values are greater than Zero

OUTPUT RESULTS
Comment:
Position of Centroid
Distance of P1 from Centroid (m):
Distance of P2 from Centroid (m):
Distance of P3 from Centroid (m):
Trials for Absolute Maximum Bending Moment
Trial-1: Maximum BM under Load P1 Distance of P1 from A (m):
Ordinate of ILD under P1 (kNm):
B.M. due to P1 (kNm):
Distance of P2 from A (m):
Ordinate of ILD under P2 (kNm):
B.M. due to P2 (kNm):
Distance of P3 from A (m):
Ordinate of ILD under P3 (kNm):
B.M. due to P3 (kNm):
Trial-1 Max. BM under P1 (kNm):
Trial-2: Maximum BM under Load P2 Distance of P1 from A (m):
Ordinate of ILD under P1 (kNm):
B.M. due to P1 (kNm):
Distance of P2 from A (m):
Ordinate of ILD under P2 (kNm):
B.M. due to P2 (kNm):
Distance of P3 from A (m):
Ordinate of ILD under P3 (kNm):
B.M. due to P3 (kNm):
Trial-2 Max. BM under P2 (kNm):
Trial-3: Maximum BM under Load P3 Distance of P1 from A (m):
Ordinate of ILD under P1 (kNm):
B.M. due to P1 (kNm):
Distance of P2 from A (m):
Ordinate of ILD under P2 (kNm):
B.M. due to P2 (kNm):
Distance of P3 from A (m):
Ordinate of ILD under P3 (kNm):
B.M. due to P3 (kNm):
Trial-3 Max. BM under P3 (kNm):
Absolute Max. BM (kNm):
Absolute Max. occur under :
Point of Absolute Max. BM from A (m):

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