The author is not wrong, but it is a bit confusing. Your method yields the rather low average shear stress along the entire over 200mm full width of the flange, while the solution yields the much higher shear stress in the 19.6mm flange thickness into the page. If you imagine that the the 108 mm portion of the flange was broken off from point a to the right end, and you wanted to glue it back on, you'd need a high strength glue, whereas if the full 200 mm width of flange was broken off from the top to point a and you wanted you wanted to glue it back on , you need only a low strength glue. These shear flow concepts are not explained that well in many texts , and are difficult to understand.fonseh said:
how do we know whether the shear stress yield is small or large ?PhanthomJay said:
We're not talking shear yield stress we are talking actual shear stress under the given load. The solution gives 16 MPa in the flange at section a. That is higher than the shear stress averaged over the flange width which by your approach comes out to maybe on the order of 3 MPa, which is a lot lower than 16. Both stresses are well below steel yield shear stresses.fonseh said:
Do you mean if follow my approach , the ans is 3 MPa, which is a lot lower than 16. Then , it's wrong ? why it is so ?PhanthomJay said:
The issue is that the 3 MPa shear stress in the flange calculated by your method is the average shear stress over the entire 200 mm width of the flange. Actual shear stress varies from 0 at the left end to a max at the center then back to 0 at the right end of the flange. Shear stresses are calculated at a plane, not a point. The solution gives the shear stress at a plane into the page cut by the vertical dotted line through point a. Your's gives the average shear stress at a plane cut by a horizontal line running at the bottom of the flange. As I mentioned, these are difficult concepts to grasp.fonseh said:
Yes, the peak of the triangle corresponds to the 16 MPa value . You should note that the direction of this shear stress is to the left , not vertical, and if you are familiar with the equilibrium of the 3D stress cube, the stress must also act longitudinally into the plane of the page.fonseh said:
how to determine whether it is horizontal or vertical stress acting ?fonseh said:
Both vertical and horizontal shear stresses are acting on the flange, and each has a longitudinal shear stress associated with it.fonseh said:
Here's from my lecturer ,PhanthomJay said:
you cut the flange vertically to determine horiz and complimentary longitudinal shear stress. You cut the flange horizontally to determine vert and complimentary longitudinal shear stress.fonseh said:
where does the longitidunal stress act ? in which direction ? can you draw it out ? i am confusedPhanthomJay said:
why ?PhanthomJay said:
so , only vertical shear stress acting on the beam ?PhanthomJay said:
You are calculating ybar = 2.5 from the vertical axis, but you should be looking at ybar from the horizontal neutral axis, which is 0.fonseh said:
vertical and complimentary longitudinal, no horizontal.fonseh said:
ok , why we need to calculate ybar from horizontal neutral axis ?PhanthomJay said:
See post 19. Say you have a 10 by 10 cross section. Max vert shear stress is at neutral axis and using area above neut axis, Q is (10)(5)(2.5) = 125 . For max horiz shear stress , using area to the right of the vert axis of the shape, Q is (5)(10)(0) = 0.fonseh said:
PhanthomJay said:
Loading is vertically applied, so you use the horizontal neutral axisfonseh said:
Shear stress is a type of stress that occurs in a material when it is subjected to forces that cause one part of the material to slide relative to another part. In a beam, shear stress is the force per unit area that acts parallel to the cross-sectional area of the beam at a specific point.
Shear stress can be calculated using the formula: τ = VQ/It, where τ is the shear stress, V is the shear force acting at the point, Q is the first moment of area of the cross-section of the beam above the point, I is the moment of inertia of the entire cross-section, and t is the thickness of the beam.
The factors that can affect shear stress at a point in a beam include the magnitude and direction of the applied load, the cross-sectional shape and dimensions of the beam, and the material properties of the beam such as its modulus of elasticity and shear modulus.
Shear stress is important in beam design because it can affect the stability and strength of a beam. If the shear stress exceeds the material's shear strength, it can cause the beam to fail. Therefore, it is crucial to calculate and consider shear stress in the design process to ensure the beam can withstand the expected load.
Shear stress can be reduced at a particular point in a beam by increasing the cross-sectional area of the beam, changing the shape of the beam to distribute the load more evenly, or adding structural supports such as braces or stiffeners. Additionally, using materials with higher shear strength can also help reduce shear stress at a specific point.
