36 Elongation is the conditions of strength and uniformity in compression After determining the tension in the dangerous section of the stretching (compressing) boom and determining the allowable stress for the boom material, it is possible to conclude about the strength of the boom. For this, the stress in the dangerous section is compared with the allowable stress for the stem material.
(3.33)
If the mast material has different resistance to elongation and compression, the strength calculation is done separately for elongation and separately for compression as follows.
three types of problems can be solved using the consistency condition :
1. Checking the stability of the existing construction . In this case, the actual stress is calculated according to the magnitudes of the external forces and the dimensions of the cross-section, and compared with the permissible stress:
(3.34)
should not differ by 5% from the permissible stresses . The actual overvoltage cannot be allowed to differ more than this value from the point of view of strength. A decrease of more than 5% indicates that the material is being used excessively.
Actual strength safety factor for plastic materials n= white / ; for brittle materials n= v / . Here is the real tension in the cross section of the rod.
2. Determining the safe magnitude of the external force.In this case, the load-bearing capacity of the existing structure is determined by the dimensions of the cross-section and the allowable stress values for the material of the structure.
(3.35)
3. The issue of design, that is, finding the necessary dimensions of the cross section. It is based on the known values of external forces and the allowable stress magnitude for the selected material.
(3.36)
Distribution of tensile stresses in rectangular and I-beam sections. (Juravsky's formula, rectangle,parabola, maximum value, compound, shelf, wall, stability condition).
The distribution of tensile stresses in rectangular and I-beam sections can be analyzed using various methods, including Juravsky's formula, which is commonly used in engineering calculations. Let's discuss the concepts related to the distribution of tensile stresses in these sections.
Rectangular Section: When a rectangular section is subjected to tensile loads, the stress distribution is relatively straightforward. The stress is uniform across the entire cross-section, with the maximum stress occurring at the extreme fibers (top and bottom) of the section. This distribution can be represented by a rectangular-shaped stress profile.
Juravsky's formula, also known as the Modified Compression Field Theory (MCFT), can be used to calculate the ultimate moment capacity of reinforced concrete rectangular sections. It considers the nonlinear distribution of concrete compression and the linear distribution of tension reinforcement. The formula incorporates various parameters such as concrete strength, reinforcement properties, and section geometry to estimate the moment capacity.
I-Beam Section: An I-beam section consists of a web (vertical member) and flanges (horizontal members) at the top and bottom. The distribution of tensile stresses in an I-beam section is more complex compared to a rectangular section due to the presence of flanges and web.
The stress distribution in the flanges is similar to that in a rectangular section, with maximum stresses occurring at the extreme fibers. However, in the web, the stress distribution follows a parabolic shape, with the maximum tensile stress occurring at the center of the web. This parabolic distribution accounts for the varying distance of each point in the web from the neutral axis.
Maximum Value of Tensile Stress: The maximum value of tensile stress occurs at the extreme fibers of the section, whether it's the top and bottom fibers in a rectangular section or the flange fibers in an I-beam section. These extreme fibers experience the highest tensile forces and therefore bear the maximum stress.
Compound Sections: Compound sections are formed by combining different basic shapes, such as rectangles and I-beams. In these cases, the stress distribution depends on the arrangement and combination of the individual sections. The stress distribution can vary across different regions of the compound section, and it may require more complex analysis methods to determine the exact stress distribution accurately.
Stability Conditions: In designing structural members, stability conditions play a crucial role. Stability conditions ensure that the cross-section can resist the applied loads without experiencing excessive deformations or failure. For rectangular and I-beam sections, stability conditions consider factors such as the slenderness ratio, bracing conditions, and buckling behavior to determine the section's stability under tensile loads.
Shelf and Wall Sections: Shelf and wall sections refer to specific types of rectangular sections used in structural engineering. A shelf section is a relatively thin rectangular section, primarily designed to support loads in a perpendicular direction to the shelf's length. A wall section, on the other hand, has a larger thickness and is designed to withstand loads parallel to its length. The distribution of tensile stresses in these sections is similar to that in a standard rectangular section, with the maximum stress occurring at the extreme fibers.
