Problem 4: Design a walkway to span a newly installed pipeline in your plant. Compute the the maximum allowable uniformly distributed load it could carry while limiting the stress due to bending to one-fifth of the ultimate strength. Problem 3: The figure shows the cross-section of a beam built from aluminum 6061-T6. Assuming that the load acts at the center of the beam, calculate the required section modulus of the beam to limit the bending stress to 140 MPa then select the lightest SI W-beam that satisfies the criteria. Each beam carries the weight of 20 m Sch 40 DN-600 pipe (see PanGlobal Academic Extract), filled with oil of 0.9 SG. Problem 2: A pipeline is simply supported above ground on horizontal beams, 4.5 m long.

Does this construction meet the design requirements? AISC recommends that the maximum bending stress for building-like structures under static loads be kept below 0.66×S y. The beam is constructed using W200×100 I-beam profile from AISI-1020 cold rolled material. Problem 1: A simply supported beam, 9.9 meters long, is loaded with concentrated loads as follows: Note: if not specified, use σ design = 0.6×σ YS, where σ YS is the Yield Strength, from textbook Appendix B.

no twisting, buckling or crippling occurs.

if the material has different strengths in tension and compression (example cast iron or other anisotropic materials) then separate calculations are required for both tension and compression surfaces.

the beam material is homogeneous and has equal strength in tension and compression.

the resulting stress is below the limit of proportionality of the material.

all the loads act perpendicular to the longitudinal axis of the beam.

the beam is straight, relatively long and narrow and of uniform cross-section.

The flexure formula is valid if the following criteria are met:

Z x is called section modulus and is a term that combines the moment of inertia and the distance to the extreme fiber ( Z x = I x / c).

c is the maximum distance from the centroidal axis to the extreme fiber (again, this can be to the top or bottom of the shape).

I x is the moment of inertia about x (horizontal) centroidal axis.

if the maximum bending stress is required then M is the maximum bending moment acting on the beam.

M is the bending moment along the length of the beam where the stress is calculated.

σ max is the maximum stress at the farthest surface from the neutral axis (it can be top or bottom).

Retrieved 14 February 2017.To determine the maximum stress due to bending the flexure formula is used: University of Arizona Opto-Mechanical Papers Reference. 'Flexure Mounts for High Resolution Optical Elements' (PPT).

'Application of Flexure Structures to Active and Adaptive Opto-Mechanical Mechanisms' (PDF). 'Three-degree-of-freedom flexure-based manipulator for high-resolution spatial micromanipulation'. : Cite journal requires |journal= ( help) 'Eliminating Underconstraint in Double Parallelogram Flexure Mechanisms'. Additionally, special care must be taken to design the flexure to avoid material yielding or fatigue, both of which are potential failure modes in a flexure design. This makes flexures a critical design feature used in optical instrumentation such as interferometers.ĭue to their mode of action, flexures are used for limited range motions and cannot replace long-travel or continuous-rotation adjustments. Flexures are able to achieve much lower resolution limits (in some cases measured in the nanometer scale), because they depend on bending and/or torsion of flexible elements, rather than surface interaction of many parts (as with a ball bearing). Additionally, conventional bearings or linear slides often exhibit positioning hysteresis due to backlash and friction. High precision alignment tasks might not be possible when friction or stiction are present. In the field of precision engineering (especially high-precision motion control), flexures have several key advantages. Using compound flexures, complex motion profiles with specific degrees of freedom and relatively long travel distances are possible. Since single flexure features are limited both in travel capability and degrees of freedom available, compound flexure systems are designed using combinations of these component features.

The flexture formula