Contents
When is the structure of an equation statically determinate?
For each case, a mathematical equation is formed. If the number of equations = the number of unknowns, then the structure is statically determinate. If, on the other hand, number of equations < the number of unknowns, the structure is statically indeterminate, and hence, other methods need to be used to analyze it.
Why are beams 1 and 2 statically determinate?
In the figure above, the beams number 1 and 2 are statically determinate structures due to the following reasons: 1- Beam number 1: the number of unknown forces is 3 = the number of equations is 3. 2- Beam number 2: the number of unknown forces is 3 = the number of equations is 3.
How to calculate the shear and moment diagram?
But the procedure is exactly the same to determine . Taking the sum of the moments about the cut and again assuming clockwise moments are positive, Now we can use equation (12) to determine the value of the internal bending moment for any value of along the beam. Plotting the bending moment diagram is simply a matter of plotting the equation.
How is shear force related to bending moments?
Building on our discussion of bending moments, the shear force represented in the shear force diagram is also the resultant of shear stresses acting at a given point in the structure. Consider the cut face of the beam discussed above.
How are determinate and indeterminate structures analysed?
Determinate structures are analysed just by the use of basic equilibrium equations. By this analysis, the unknown reactions are found for the further determination of stresses. Redundant or indeterminate structures are not capable of being analysed by mere use of basic equilibrium equations.
What makes a truss an indeterminate or determinate structure?
A truss is statically determinate internally if the total number of members. m=2j – 3. where j= number of joints. A truss having more than (2j – 3) members is statically indeterminate or redundant, the degree of indeterminacy or redundancy being equal to the number of extra members.