Answer is provided, (29 MPa), but need to see the work. Uses the thin-walled ass
ID: 1848756 • Letter: A
Question
Answer is provided, (29 MPa), but need to see the work. Uses the thin-walled assumption.
A racing bicycle has a handlebar made of high strength steel (Young's modulus E = 210 GPa, Poisson ratio v = 0.3). The handlebar is a hollow circular cylinder, 50 cm long and 2 cm in diameter with wall thickness 2 mm. The handlebar is clamped to the frame at its midpoint. A rider loads each end of the bar with quarter of her 55 kg mass. She grips the racing handlebar such that the weight transferred to each end is at a radial distance of 10 cm from the cylindrical axis and at half the handlebar's length from the clamp. What is the maximum shear stress and where does it occur? (29MPa)Explanation / Answer
How to Calculate Max Shear Stress Shear stress is the distribution of shear force over an area. Any force that acts on a plane in a parallel direction is a shear force. If you hold a pencil in two tightly clenched fists and try to slide them past each other, you apply shear force along the pencil's cross-section. When an object fails under shear stress, the pieces will slide past each other, rather than pulling apart or crunching together. Under a force with uniform direction, shear stress will be greatest at the cross section's midpoint and weakest at its edges. Calculate the shear force acting on the cross-section. Do this by drawing the object and schematically cutting it along the cross section you want to analyze. If the object is static, the sum of forces acting in any direction will be zero. If there are two downward forces of 50 pounds acting on a beam to the left of a certain point, there must be a single upward force of 100 pounds acting within the beam at that cross section, because 100 - 50 - 50 = 0. Identify the cross-section's neutral axis--the point where maximum shear stress will occur. For symmetrical shapes such as a rectangle or circle, the neutral axis simply runs through the midpoint between the top and bottom of the cross section. For more complex shapes, use the formula At*yc = A1*y1 + A2*y2 + A3*y3.... , where A1, A2 and A3 are the areas of sub-shapes that make up the cross section, and y1, y2 and y3 are the distances to the centroids of those subshapes. The variable At represents the total area, and yc represents the distance to the neutral axis. Solve this formula for yc.
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