12.10:
Indeterminate Structure
In an indeterminate structure, the static equilibrium equations cannot sufficiently determine the internal forces and reactions on it.
Consider a wobbling table with four cylindrical legs, each having a cross-sectional area of 1 cm2. The length of three legs is 2 m, while the fourth leg is longer by 0.50 mm. When a mass of 300 kg is placed, the legs are compressed, and the table is level and no longer wobbles. If the Young's modulus of the wooden legs is 1.3 x 1010 N/m2, determine the magnitudes of the forces acting on the legs.
Recalling the Young's modulus equation, a relationship between the elongated leg and the shorter legs can be established.
By balancing all the vertical forces acting on the system, the force on the elongated leg can be obtained.
Comparing the equations of the elongated leg and substituting the values, the force on the shorter legs can be determined.
By using the force equation and substituting the values, the force acting on the elongated leg can be obtained.
12.10:
Indeterminate Structure
Indeterminate structures refer to structures where internal forces and reactions cannot be determined using only the equations of static equilibrium. Indeterminate structures have more unknown forces and reaction forces than equations of static equilibrium that can be used to determine them. Indeterminate structures are often used in engineering to create complex, efficient, and aesthetically pleasing structures. There are various types of indeterminate structures used in engineering and some examples are listed below:
Suspension bridges are an excellent example of indeterminate structures, as they require advanced analysis techniques to determine the forces and reactions. They consist of cables suspended between towers that support the weight of the bridge deck. The cables are in tension, while the towers are in compression, making them indeterminate structures.
Cantilever bridges are another example of indeterminate structures. They consist of two anchored supports with a central span that is supported by cantilever arms. The cantilever arms are under bending stress, and the supports are under compressive stress, making cantilever bridges indeterminate structures.
Domes are structures that are curved in shape and can span large areas without requiring intermediate supports. They are used in buildings such as stadiums, observatories, and religious structures. Domes are indeterminate structures because they are subject to multiple forces, including bending and compression.
Multistory buildings are structures that consist of multiple floors supported by columns and beams. They are indeterminate structures because the loads from each floor are distributed to the columns and beams in a complex way, requiring advanced analysis techniques to determine the forces and reactions.
There are various methods used to solve indeterminate structures, including the force method, the displacement method, and the flexibility method. Each method involves creating additional equations to solve for the unknown forces and reactions. Designing indeterminate structures can result in efficient and cost-effective solutions due to their ability to carry large loads with minimal materials. They also require more advanced analysis techniques and calculations to determine the forces and reactions.
Suggested Reading
- Halliday & Resnick, Fundamentals of Physics Pg 364-365.