discussion bending moment
Sohar University
Faculty of Engineering
Strength of Materials
Laboratory Manual
MECH2308
Lab experiment # 3
Thick cylinder
Introduction:
Thick -walled structures are widely used in .a viatiofi, chemistry, shipbuilding, vehicle nuclear and civil engineering and many other practical .and high-technology industries. The failure of the structures caused by elastoplastic buckling has attracted a .lot of attention of the researchers of mechanics and mechanical designers, for a long period. In the past several decades, great efforts have been made but this prot;lem is still far from been completely solved. Since the elastoplastic buckling of the structures involves no proportional loading, unloading processes and localization of deformation caused by the imtberfection of the materials and structures, it is necessary to use realistic constitutive relation in this kind of analysis
Objectives:
1- To determine the experiment value of stress in three direction axial, radial and tangential. 2- To calculate the theoretical stress. 3- To plot a graph that compares experiment and theoretical value of stress.
Theory:
If a thick –walled vessel is placed under internal pressure, a axial stress state is created in the walling.The axial stress state incorporates radial, tangential and axial stresses and their magnitudes are obtained by the following formula:
When the cylinder to be studied has a r/t ratio of less than 10 (often cited as 20) the thin-walled cylinder equations no longer hold since stresses vary significantly between inside and outside surfaces and shear stress through the cross section can no longer be neglected.
In order to calculate the stresses and strains here a set of equations known as the Lamé equations must be used.
where
A and B are constants of integration, which may be discovered from the boundary conditions r is the radius at the point of interest (e.g. at the inside or outside
Faculty of Engineering
Strength of Materials
Laboratory Manual
MECH2308
Lab experiment # 3
Thick cylinder
Introduction:
Thick -walled structures are widely used in .a viatiofi, chemistry, shipbuilding, vehicle nuclear and civil engineering and many other practical .and high-technology industries. The failure of the structures caused by elastoplastic buckling has attracted a .lot of attention of the researchers of mechanics and mechanical designers, for a long period. In the past several decades, great efforts have been made but this prot;lem is still far from been completely solved. Since the elastoplastic buckling of the structures involves no proportional loading, unloading processes and localization of deformation caused by the imtberfection of the materials and structures, it is necessary to use realistic constitutive relation in this kind of analysis
Objectives:
1- To determine the experiment value of stress in three direction axial, radial and tangential. 2- To calculate the theoretical stress. 3- To plot a graph that compares experiment and theoretical value of stress.
Theory:
If a thick –walled vessel is placed under internal pressure, a axial stress state is created in the walling.The axial stress state incorporates radial, tangential and axial stresses and their magnitudes are obtained by the following formula:
When the cylinder to be studied has a r/t ratio of less than 10 (often cited as 20) the thin-walled cylinder equations no longer hold since stresses vary significantly between inside and outside surfaces and shear stress through the cross section can no longer be neglected.
In order to calculate the stresses and strains here a set of equations known as the Lamé equations must be used.
where
A and B are constants of integration, which may be discovered from the boundary conditions r is the radius at the point of interest (e.g. at the inside or outside