Shear Force and Bending Moment Calculator (Simply Supported Beam with Central Point Load)
Understanding shear force and bending moment is fundamental in structural engineering. These internal forces and moments develop within a beam due to external loads and are crucial for designing safe and efficient structures. A Shear Force Diagram (SFD) graphically represents the variation of shear force along the length of a beam, while a Bending Moment Diagram (BMD) illustrates the variation of bending moment.
What are Shear Force and Bending Moment?
- Shear Force: This is the internal force acting perpendicular to the beam's longitudinal axis. It represents the tendency of one part of the beam to slide past the adjacent part. High shear forces can lead to shear failure.
- Bending Moment: This is the internal moment acting about the beam's longitudinal axis. It represents the tendency of the beam to bend or rotate. High bending moments can lead to flexural (bending) failure.
Engineers use SFDs and BMDs to identify critical sections in a beam where shear force or bending moment are maximum. These maximum values are then used to select appropriate beam dimensions and materials to ensure the structure can withstand the applied loads without failure.
About This Calculator
This calculator is designed for a specific, common scenario: a simply supported beam subjected to a single point load applied exactly at its center. A simply supported beam is supported by a pin connection at one end and a roller connection at the other, allowing for rotation but preventing vertical movement. The central point load creates a symmetrical loading condition, simplifying the calculations.
Formulas Used:
For a simply supported beam of span 'L' with a central point load 'P':
- Reactions at Supports (RA, RB): RA = RB = P / 2
- Maximum Shear Force (Vmax): Vmax = P / 2 (occurs just inside the supports)
- Maximum Bending Moment (Mmax): Mmax = (P × L) / 4 (occurs at the center of the beam)
Enter the beam's span and the central point load to calculate the support reactions, maximum shear force, and maximum bending moment.
Example Calculation:
Let's consider a simply supported beam with a span of 8 meters (L = 8 m) and a central point load of 40 kilonewtons (P = 40 kN).
- Support Reactions: RA = RB = 40 kN / 2 = 20 kN
- Maximum Shear Force: Vmax = 40 kN / 2 = 20 kN
- Maximum Bending Moment: Mmax = (40 kN × 8 m) / 4 = 320 kNm / 4 = 80 kNm
This means each support will carry a vertical load of 20 kN, the maximum shear force within the beam will be 20 kN, and the maximum bending stress will occur at the center of the beam, corresponding to a bending moment of 80 kNm.
Interpretation of Results:
- Support Reactions: These are the forces exerted by the supports on the beam to keep it in equilibrium. They are essential for designing the supports themselves.
- Maximum Shear Force: This value indicates the highest shear stress the beam will experience. It's critical for checking the beam's resistance to shear failure, especially for short, deep beams.
- Maximum Bending Moment: This is the most critical value for flexural design. It determines the required depth and material strength of the beam to prevent bending failure, which is common in longer, shallower beams.
Always remember that this calculator provides values for a specific, simplified case. Real-world structural analysis often involves more complex loading conditions, beam types, and material properties, requiring advanced engineering software and expertise.
function calculateShearBending() { var beamSpan = parseFloat(document.getElementById('beamSpan').value); var pointLoad = parseFloat(document.getElementById('pointLoad').value); var resultDiv = document.getElementById('result'); if (isNaN(beamSpan) || isNaN(pointLoad) || beamSpan <= 0 || pointLoad <= 0) { resultDiv.innerHTML = 'Please enter valid positive numbers for Beam Span and Central Point Load.'; return; } // Calculations var reactionA = pointLoad / 2; var reactionB = pointLoad / 2; var maxShearForce = pointLoad / 2; var maxBendingMoment = (pointLoad * beamSpan) / 4; resultDiv.innerHTML = '