1. Concepts about the science of "Strength of Materials" tasks, consistency, uniformity, priority, brief history

Shell is a plate wchich curved in the middle (Fig. 1.6, b). Shells include aircraft and missile fuselages, building domes, submarine hulls, thin-walled tanks, etc.
A massive balanced bodyIt refers to a solid body with three dimensions in the same order (Fig. 1.6, c ). These include building foundations, bridge supports, retaining walls, etc.
In the construction elements and details of the machine, there are many constructions made from the interconnection of beams, examples of which are trusses and frames.
Truss refers to a geometrically invariant system formed by connecting the rods to hinges based on a certain law. When external forces are applied to the nodes of the farm, its single nodes are conditionally replaced by hinges. Truss elements mainly resist compression or stretching (Figure 1.7).
Frameis asystem formed by the interconnection of rods working on compression (tension) and bending (Fig. 1.8).
The vertical struts in the Ramani are called pillars, and the horizontal struts are called rigels. Ramani bikr knots restrict the twists of the rods attached to them, that is, the angles between the rods attached to the knot do not change.
The science of resistance of materials deals with the calculation of rough and thin-walled steels. The theory of elasticity and plasticity deals with the calculation of plate, plastic, shell and weighted bodies.


4-5-38Distribution of tensile stresses in rectangular and I-beam sections. Checking the strength of beams to test stresses (Juravsky's formula, rectangle, parabola, maximum value, joint, shelf, wall, strength condition). In our previous session, we were discussing the bending stress produced in a beam which is subjected to a pure bending. We have assumed there that beam will be subjected with a pure bending moment and shear force will be zero and hence shear stress will also be zero.In actual practice, beam will be subjected with shear force also and therefore shear stress too. Shear force and hence shear stress will vary section to section.We will see here the shear stress distribution across the various sections such as rectangular section, circular section, I section and T section. In this post, we will see shear stress distribution in rectangular section.Let us consider the rectangular section ABCD ofbeam as displayed in following figure. We have assumed one layer EF at a distance y from the neutral axis of the beam section
We have following information from above figure.
b= Width of the rectangular section
d= Depth of the rectangular section
N.A: Neutral axis of the beam section
EF: Layer of the beam at a distance y from the neutral axis of the beam section
A= Area of section CDEF, where shear stress is to be determined
ȳ = Distance of C.G of the area CDEF from neutral axis of the beam section

Shear stress at a section will be given by following formula as mentioned here

Where,
F = Shear force (N)

τ = Shear stress (N/mm²)
A = Area of section, where shear stress is to be determined (mm²)
ȳ = Distance of C.G of the area CDEF from neutral axis of the beam section (m)
I = Moment of inertia of the given section about the neutral axis (mm⁴)
b= Width of the given section where shear stress is to be determined (m)
Let us secure the value of the area of section, where shear stress is to be determined and we can write it as mentioned here
A= b x (d/2-y)
Distance of C.G of the area CDEF from neutral axis of the beam section, ȳ could be written as mentioned here
ȳ = y + (d/2-y)/2
ȳ = (d/2+ y)/2
I = bd³/12Let us use the value of above parameters in equation of shear stress and we will have
We can easily say from above equation that maximum shear stress will occur at y = 0 or maximum shear stress will occur at neutral axis and value of shear stress will be zero for the area at the extreme ends.We will also find the value of maximum shear stress and it could be easily calculated by using the value of y = 0 and therefore we will have following formula for maximum shear stress as displayed here in following figure.

As we know that average shear stress or mean shear stress will be simply calculated by dividing shear force with area and therefore we can say that
Average shear stress, τ_av= Shear force/ Area

Therefore we can say that for a rectangular section, value of maximum shear stress will be equal to the 1.5 times of mean shear stress.We can say, from equation of shear stress for a rectangular section, that shear stress distribution diagram will follow parabolic curve and we have drawn the shear stress distribution diagram for a rectangular section as displayed in following figure.