Name: axial rod reactions with redundant support
Uploaded: 2024-03-07T13:22:37.000Z
Duration: 1 min 16 s
Channel: JoVE

Consider two cylindrical rods, one of steel and another of brass, joined at point B and restrained by rigid supports at points A and C.
Determine the reactions at points A and C. Also, determine the deflection at point B.
Here, the rod structure is considered statically indeterminate as it has more supports than necessary for the condition of equilibrium, leading to an excess of unknown reactions over equilibrium equations.
So, the reaction at point C is considered redundant and released from the support. It is treated as an additional load.
Then, using the superposition method, the deformation in each section of the rod structure is determined and combined to determine the total deformation.
&#160;Considering the total deformation expression, the total deformation of the rod structure equaling zero, and the summation of all the loads equaling zero, the unknown reaction forces are determined.
The deflection at point B is calculated by summing the deformations in the sections before point B in the rod structure.

statisch onbepaalde probleemoplossing

Statically Indeterminate Problem Solving

Statisch onbepaalde problemen zijn problemen waarbij de statica alleen de interne krachten of reacties niet kan bepalen. Beschouw een structuur bestaande uit twee cilindrische staven gemaakt van staal en messing. Deze staven zijn verbonden op punt B en vastgehouden door stijve steunen op de punten A en C. Nu moeten de reacties op de punten A en C en de doorbuiging op punt B worden bepaald. Deze staafstructuur wordt geclassificeerd als statisch onbepaald, omdat de structuur meer steunen heeft dan nodig is om het evenwicht te behouden, wat leidt tot een overschot aan onbekende reacties ten opzichte van de beschikbare evenwichtsvergelijkingen.

De statische onbepaaldheid wordt opgelost door de reactie op punt C, als overbodig te beschouwen en deze van zijn steun te ontdoen. Deze overtollige reactie wordt behandeld als een extra belasting. Vervolgens wordt de superpositiemethode ingezet om de vervorming in elke sectie van de staafstructuur te bepalen. Door deze individuele vervormingen te combineren, wordt de totale vervorming expressie voor de gehele constructie afgeleid. Gezien de uitdrukkingen is de totale vervorming van de staafstructuur gelijk aan nul, en de som van alle belastingen gelijk aan nul, de onbekende reactiekrachten worden bepaald. Tenslotte wordt de doorbuiging op punt B berekend door de vervormingen in de staafstructuursecties voorafgaand aan punt B op te tellen.

Statisch onbepaalde probleemoplossing

Consider two cylindrical rods, one of steel and another of brass, joined at point B and restrained by rigid supports at points A and C.
Determine the ...

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Mechanical Engineering

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Unit 1

Stress and Strain - Axial Loading

Spanning en vervorming - axiale belasting

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axial rod reactions with redundant support

Axial rod reactions with a redundant support are found by combining equilibrium with deformation. The structure here uses two cylindrical rods, one steel and one brass, joined at point B and held by rigid supports at points A and C. The goal is to determine the reactions at A and C and the deflection at B.

This setup is statically indeterminate because the supports create more unknown reactions than the equilibrium equations can solve. Statics alone is not enough to find every internal force or support reaction. To handle this, the reaction at point C is treated as a redundant reaction, meaning it is released from its support and used as an added load.

The superposition method is then used to find the deformation in each section of the rod structure. These separate deformations are combined to form the total deformation expression for the full rod system. When the total deformation is set equal to zero, and the sum of the loads is also zero, the unknown reaction forces can be determined.

After the reactions are found, the deflection at point B is calculated by adding the deformations in the sections of the rod structure before point B. This approach shows how compatibility of deformation helps solve a problem that equilibrium alone cannot complete.

Axial Rod Reactions with Redundant Support

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statically indeterminate problem solving

Axial rod reactions with a redundant support are found by combining equilibrium with deformation. The structure here uses two cylindrical rods, one steel and one brass, joined at point B and held by rigid supports at points A and C. The goal is to determine the reactions at A and C and the deflection at B. This setup is statically indeterminate because the supports create more unknown reactions than the equilibrium equations can solve. Statics alone is not enough to find every internal force...

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key terms and concepts

Learn how a steel-brass rod system with rigid supports uses redundant reactions, superposition, and zero total deformation to find support forces and deflection at point B.

Axial Rod Reactions with Redundant Support | JoVE K12

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Axial Rod Reactions with Redundant Support

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