Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge Calculator

✖Length of Rectangular Beam is the measurement or extent of something from end to end.ⓘ Length of Rectangular Beam [Len]			+10% -10%
✖Ratio between Plastic Moments is the ratio of plastic moment at the ends to the plastic moment at the center.ⓘ Ratio between Plastic Moments [k]			+10% -10%
✖Plastic Moment is the moment at which the entire cross section has reached its yield stress.ⓘ Plastic Moment [M_p]			+10% -10%
✖Uniformly distributed Load (UDL) is a load that is distributed or spread across the whole region of an element whose magnitude of the load remains uniform throughout the whole element.ⓘ Uniformly Distributed Load [q]			+10% -10%

✖Distance of point where Moment is Maximum is the distance from a point where moment is maximum in the interior span.ⓘ Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge [x]

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Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Distance of point where Moment is Maximum = (Length of Rectangular Beam/2)-((Ratio between Plastic Moments*Plastic Moment)/(Uniformly Distributed Load*Length of Rectangular Beam))
x = (Len/2)-((k*M_p)/(q*Len))
This formula uses 5 Variables

Variables Used

Distance of point where Moment is Maximum - (Measured in Meter) - Distance of point where Moment is Maximum is the distance from a point where moment is maximum in the interior span.
Length of Rectangular Beam - (Measured in Meter) - Length of Rectangular Beam is the measurement or extent of something from end to end.
Ratio between Plastic Moments - Ratio between Plastic Moments is the ratio of plastic moment at the ends to the plastic moment at the center.
Plastic Moment - (Measured in Newton Meter) - Plastic Moment is the moment at which the entire cross section has reached its yield stress.
Uniformly Distributed Load - (Measured in Newton per Meter) - Uniformly distributed Load (UDL) is a load that is distributed or spread across the whole region of an element whose magnitude of the load remains uniform throughout the whole element.

STEP 1: Convert Input(s) to Base Unit

Length of Rectangular Beam: 3 Meter --> 3 Meter No Conversion Required
Ratio between Plastic Moments: 0.75 --> No Conversion Required
Plastic Moment: 10.007 Kilonewton Meter --> 10007 Newton Meter (Check conversion here)
Uniformly Distributed Load: 10.0006 Kilonewton per Meter --> 10000.6 Newton per Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x = (Len/2)-((k*M_p)/(q*Len)) --> (3/2)-((0.75*10007)/(10000.6*3))

Evaluating ... ...

x = 1.24984000959942

STEP 3: Convert Result to Output's Unit

1.24984000959942 Meter --> No Conversion Required

FINAL ANSWER

1.24984000959942 ≈ 1.24984 Meter <-- Distance of point where Moment is Maximum

(Calculation completed in 00.020 seconds)

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Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge

LaTeX Go Distance of point where Moment is Maximum = (Length of Rectangular Beam/2)-((Ratio between Plastic Moments*Plastic Moment)/(Uniformly Distributed Load*Length of Rectangular Beam))

Absolute Value of Maximum Moment in Unbraced Beam Segment

LaTeX Go Maximum Moment = (Bending Moment Coefficient*((3*Moment at Quarter Point)+(4*Moment at Centerline)+(3*Moment at Three-quarter Point)))/(12.5-(Bending Moment Coefficient*2.5))

Condition for Maximum Moment in Interior Spans of Beams

LaTeX Go Point of Maximum Moment = (Length of Rectangular Beam/2)-(Maximum Bending Moment/(Uniformly Distributed Load*Length of Rectangular Beam))

Ultimate Load for Continuous Beam

LaTeX Go Ultimate Load = (4*Plastic Moment*(1+Ratio between Plastic Moments))/Length of Rectangular Beam

Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge Formula

LaTeX Go

What is Plastic Hinge?

Plastic Hinge is used to describe the deformation of a section of a beam where plastic bending occurs. In plastic limit analysis of structural members subjected to bending, it is assumed that an abrupt transition from elastic to ideally plastic behaviour occurs at a certain value of moment, known as plastic moment (Mp). Member behaviour between Myp and Mp is considered to be elastic. When Mp is reached, a plastic hinge is formed in the member.

How to Calculate Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge?

Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge calculator uses Distance of point where Moment is Maximum = (Length of Rectangular Beam/2)-((Ratio between Plastic Moments*Plastic Moment)/(Uniformly Distributed Load*Length of Rectangular Beam)) to calculate the Distance of point where Moment is Maximum, The Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge formula is defined as the distance of a point from the support where the moment is maximum after the formation of a plastic hinge. Distance of point where Moment is Maximum is denoted by x symbol.

How to calculate Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge using this online calculator? To use this online calculator for Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge, enter Length of Rectangular Beam (Len), Ratio between Plastic Moments (k), Plastic Moment (M_p) & Uniformly Distributed Load (q) and hit the calculate button. Here is how the Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge calculation can be explained with given input values -> 1.250015 = (3/2)-((0.75*10007)/(10000.6*3)).

FAQ

What is Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge?

The Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge formula is defined as the distance of a point from the support where the moment is maximum after the formation of a plastic hinge and is represented as x = (Len/2)-((k*M_p)/(q*Len)) or Distance of point where Moment is Maximum = (Length of Rectangular Beam/2)-((Ratio between Plastic Moments*Plastic Moment)/(Uniformly Distributed Load*Length of Rectangular Beam)). Length of Rectangular Beam is the measurement or extent of something from end to end, Ratio between Plastic Moments is the ratio of plastic moment at the ends to the plastic moment at the center, Plastic Moment is the moment at which the entire cross section has reached its yield stress & Uniformly distributed Load (UDL) is a load that is distributed or spread across the whole region of an element whose magnitude of the load remains uniform throughout the whole element.

How to calculate Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge?

The Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge formula is defined as the distance of a point from the support where the moment is maximum after the formation of a plastic hinge is calculated using Distance of point where Moment is Maximum = (Length of Rectangular Beam/2)-((Ratio between Plastic Moments*Plastic Moment)/(Uniformly Distributed Load*Length of Rectangular Beam)). To calculate Condition for Maximum Moment in Interior Spans of Beams with Plastic Hinge, you need Length of Rectangular Beam (Len), Ratio between Plastic Moments (k), Plastic Moment (M_p) & Uniformly Distributed Load (q). With our tool, you need to enter the respective value for Length of Rectangular Beam, Ratio between Plastic Moments, Plastic Moment & Uniformly Distributed Load and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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