Type of internal forces

Type of internal forces
1. Axial and normal force
2. Shear force
3. Bending moment
4. Torsional moment or torque
Shear forces and bending moments
a. Type of external forces
1. Concentrated force (load) – forces P1, P2 and P3 in Figure1.
2. Linear distributed load – a uniformly distributed load of intensity q and q2 in Figure 1.

The resultant of a uniformly distributed load is equivalent to the area under the loading curve and acting through the centroid of this area.
b. Type of supports
1. Roller: see Figure2 (a and b)
2. External pin: see Figure2 (c and d)
3. Fixed support: see Figure2 (e and f)
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c. Types of beams

d. Sign convention
1. Internal forces

2. External forces



e. Construction of Shear and Moment Diagrams
Step 1 Determine the reaction forces and moments.
Step 2 Draw and label the vertical axes for V and Mz along with the units to be used.
Step 3 Draw the beam with all forces and moments. At each change of loading draw a vertical line.
Step 4 Consider imaginary extensions on the left and right ends of the beam. V and Mz are zero in these imaginary extensions.
Shear force diagram
Step 5 If there is a point force, then increase the value of V in the direction of the point force.
Step 6 Compute the area under the curve of the distributed load. Add the area to the value of V1 if py is positive, and subtract it if py is negative, to obtain the value of V2.
Step 7 Repeat Steps 5 and 6 until the imaginary extension at the right of the beam is reached. If the value of V is not zero in the imaginary extension, then check Steps 5 and 6 for each segment of the beam.
Step 8 Draw additional vertical lines at any point where the value V is zero. Determine the location of these points by using geometry.
Step 9 Calculate the areas under the V curve and between two adjacent vertical lines.
Moment diagram
Step 10 If there is a point moment, and then use the moment template and the template equation to determine the direction of the jump.
Step 11 To move from the right of one vertical line to the left of the next vertical line, add the areas under the V curve if V is positive, and subtract the areas if V is negative.
Step 12 Repeat Steps 10 and 11 until you reach the imaginary extension on the right of the beam. If the value of Mz is not zero in the imaginary extension, then check Steps 10 and 11 for each segment of the beam.