If q - 0 , k f - 1 and the material Is insensitive to the effects of the stress concentration. If q - 1 , lc f - k t and the material is fully sensitive to the effects of the stress concentration. Some of the ways to overcome the damaging effects of localized stresses are listed as follows:. Reducing the abruptness of the change in cross-section of the member by use of fillets, etc. Reducing the value of the stress concentration by making the portion of the member in the neighborhood of the stress concentration less stiff; this sometimes may be done by substituting a member made of material with a lower modulus of elasticity, such as replacing a steel nut on a steel bolt by a bronze nut for reducing the stress concentration at the threads of the steel bolt.
Increasing the fatigue strength of the material by cold-working the portions of the members where the stress concentrations occur: For example, by the cold rolling of fillets and of bearing surfaces on axles, by the shot blasting or shot peenlng of surfaces of machine parts.
Increasing the fatigue strength of the material by alloying or heat treating. Heat treating to a certain point will increase the fatigue strength. Heat treating beyond this point might actually reduce the fatigue strength. It may be necessary to design for the Increase in stress by using a lower allowable.
Some additional methods of decreasing stress concentration are shown on the following pages. The number stamp should be called out on the una tressed or the low stressed portion of the part, or raised bosses should be provided. Other types of marking are available and should be used If possible.
Grain direction should be parallel to the load Imposed on the part whenever possible. Low endurance limits are typical of specimens tested normal to the grain. Avoid sharp bends and Internal corners.
When a sharp corner is necessary to accommodate a part which has a small radius, a stress relieving groove can be uaed effectively. Additional well placed grooves at "A" help to relieve the stress concentra- tions caused by "B". Avoid the use of large collars. Small collars do not disrupt the stress flow appreciably.
A stress relieving hole lightens the shackle and may Increase the allowable stress. Never use sharp re-entrant angles or notches In a part subjected to repeated loading. Use a faired line as shown. Heat treating will raise the static strength of the part but it will not necessarily in- crease its fatigue strength.
Avoid carrying loads around "corners" of angles, zees, etc. Avoid welded parts such as that in the figure. The part will fail at a rather low repeated stress around the weld regard- less of which member is loaded. Where members are under re- peated loads avoid all welds which induce abrupt changes in cross section. Low endurance limits are typical for 3uch specimens. Radius of Groove, r, in. Notch Radius, r, in. Fia 10,5. Hayes, J. Lugs are connector-type elements widely used as structural supports fot pin connections.
In the past, the lug strength was overdesigned since weight and sixe requirements were for the most part unrestricted. How- ever, the refinement of these requirements have necessitated conservative methods of design. This section presents static strength analysis procedures for uniformly loaded lugs and bushings. Cor double shear joints, and for single shear joints, subjected to axial, transverse, or oblique loading.
Also listed is a section which applies to lugs made from materials having ultimate elongations of at least 5T« in any direction in the plane of the lug. Cross grain tensile ultimate stress of lug material Croae grain tensile yield stress of lug material Allowable ultimate bearing stress, MHB5 Allowable yield bearing stress, MHB5 Ultimate tensile stress.
Axially loaded lugs in tension must be checked for bearing strength and for net-section strength. The bearing strength of a lug loaded in tension, as- shown in Figure S hoop-tension. The net-section of the lug through the pin must be checked against failure. In addition, the lug and bushing must be checked to ensure that the deformations at design yield load are not excessive.
Actual lug failures may involve more than one failure mode t but. J -Inch iMch or Itilckar aluminum alloy plala. AnaddlllonatM S ol 0. Equations a and b apply only if the load is uniformly dis- tributed across the lug thickness. If the pin is too flexible and bends excessively, the load on the lug will tend to peak up near the shear faces and possibly cause premature failure of the lug. A procedure to check the pin bending strength in order to pre- vent premature lug failure is given in Section 9.
Net Tension Stress Coefficient conduced. The strength of a joint such as the one shown in Figure depends on the lug-bushing ultimate strength P. For the symmetrical joint shown la the figure, Equation is used to calculate the ultimate load for the outer Lugs and bushings 2 P.
The pin ultimate shear load P mt for the symmetrical joint shown in Figure is the double shear strength of the pin:. Although actual pin bending failures are infrequent, excessive pin deflections can cause the load in the lugs to peak up near the shear planes instead of being uniformly distributed across the lug thickness, thereby leading to premature lug or bushing failures at loads less than those predicted by Equation At the same time, however, the con- centration of load near the lug shear planes reduces the bending arm and, therefore, the bending moment in the pin, making the pin less critical in bending.
The following procedure is used in determining the pin ultimate bending load. For the symmetrical joint shown in Figure 9. The pin ultimate bending load F lb? The allowable load for the joint P ul can be determined by going directly to EquHtion 9- 19a.
If P, H Equation i. However, ,uch a pin may deflect. The portion, of th. The new increa. At this point w. The following equation, give th« "balanced de. The value of F mk on the right hand aide of Equation and th. Equations and The allowable joint ultimate load P, n for the double-shear joint is obtained as follows:. Equation a. If Equation 9- 19a has been used to determine the joint allowable load, then we have a conation where the load in the lugs and tangs is assumed uniformly distributed.
The allowable stress in the tangs is F t , T. The lug tang. U Equation 9- 19b wa. Ible "a! The amount of bending can be. Figure The individual values of M and Mj are determined from the loading of the lugs as modified by the deflection, if any, of the lugs, according to the principles of mechanics.
The strength analysis procedure outlined below applies to either lug. The joint strength is determined by the lowest of the margins of safety cal- culated for the different failure modes defined by Equations through The bearing stress distribution between lug and bushing is assumed to be similar to the stress distribution that would be obtained in a rectangular cross section of width D and depth t f subjected to a load Pi and moment M At ultimate load the maximum lug bearing stress F fcF M L is approximated by.
At ultimate load the nominal value of the outer Tiber tea-ile. The bearing. At ultimate bu. The maximum value of pin. At the lug ultimat.
Determine the static strength of an axially loaded, double shear joint, auch as shown in Section 9. C Pin Bending Strength Equation The new value of pin bending atrength ia, then,. Therefore, the lug tangs are not critical and the allowable joint load remains at pounds. The transversely loaded lug. Figure illustrates the different lug dimensions are critical in determining the lug strength. Schematic of Lugs Under Transverse Loads o. The nomograph i. The interaction with Une A i.
Next connect the h 3 and h 4 Une. The different edge distance. The di. U the lug i. In concentric lug. The allowable lug tran. If the lug i. A3, and A 4 are the area, of the section, defined by h v h 2. The allowable bearing. The allow- able bu. Equations through ' can be used; however, the maximum lug bearing stresses at ultimate and yield loads must not exceed those given by Equations and The previous discussion on double shear joint applies to single shear joint strength analysis except the equations to be used are now Equations through The analysis procedures used to check the strength of axially loaded lugs and of transversely loaded lugs are combined to analyze obliquely loaded lugs such as the one shown in Figure The allowable ultimate value of P a is P a and its axial and transverse components satisfy the following equation: 1.
The allowable load curve defined by Equation is plotted on the graph in Figure P and P tr. The strength calculations are basically the same as those for an axially loaded joint except that the maximum lug bearing stress at ultimate load must. The previous discussion on double shear joints applies to single shear joint strength analysis except the equations to be used are now Equations through This distribution is based on the assumption of plastic behavior at ultimate load of the lugs and clastic bending of the pin, and gives approximately zero bending deflection of the pin.
This section presents procedures for the optimized design of lugs, bushings and pin in a symmetrical, double-shear joint, such as shown in Figure , subjected to a static axial load P. One design procedure applies to the case where the pin is critical in shear, the other to the case where the pin is critical in bending. A method is given to help determine which mode of pin failure is more likely, so that the appropriate design procedure will be use. Portions of the design procedures may be useful in obtaining efficient designs for joints other than symmetrical, double- shear joints.
An indication of whether the pin in an optimized joint design is more likely to fail in shear or in bending can be obtained from the value of R Equa- tion If R is less than 1. If R is greater than 1.
The value of F wul can be approximated by the lowest of the following three values:. F,, is the compressive yield stress of the bushings. The lug is assumed not critical in net tension, and the bushing is assumed not critical in bearing. The allowable loads for the different failure modes lug bearing failure, lug net-tension failure, and bushing failure are determined from -equations The required male and female lug thicknesses are determined by equating the applied load in each lug to the critical failure load for the lug.
If the allowable bushing load Equation is less than the allow- able lug load Equation , a reduced value of e. The n-evtously calculated pin diameter and lug thicknesses are unchanged.
If the lug net-tension strength Equation exceeds the bearing rength Equation , the net-section width can be reduced by the ratio of ne bearing strength to the net-tension strength. This approxi- mation becomes more accurate when there are no bushings and when there is no gap between lugs.
The lug is assumed not critical in tension and the bushing is assumed not critical in bearing. The lowest of these loads is critical. The first approximation to the required male and female lug thick- nesses are determined by equating the applied load in each lug to the lowest allowable load for the lug. The second approximation to the pin diameter is obtained by sub- stituting the first approximation lug thicknesses into Equation Aji average value, however, is generally sufficient.
If the final optimum value is not a standard pin diameter, choose the next larger standard pin? The final lug thicknesses corresponding to the standard pin and ' bushing are then determined. The pin diameter and lug thicknesses are unchanged. If the lug net-tension strength Equation exceeds the lug bear- ing strength Equation , the net-section width can be reduced by the ratio of the bearing strength to the net-tension strength.
Using the same materials for the lug, bushing and pin as mentioned in Section 9. Ze but the final minimum weight design will not necessarily be concentric.
Pin Failure Mode Equation The pin is first checked to determine whether it will be critical in shear or bending, using Equation The lug tension strength Equation exceeds the bushing strength Equation for the male lug.
The lug net-section tension strength Equation exceeds the hearing strength Equation for both the male and female lugs Therefore, the widths can be reduced as follows:. This section describes procedures for calculating reductions in strength for lugs made from materials which do not meet the elongation requirement.
In addition to using these procedures, special consideration must be given to possible further loss in strength resulting from material defects when the short transverse gain direction of the lug material is in the plane of the lug.
The procedure for determining net-section allowables is the same for all values of The graphs in T'gure are used to obtain a value of K. If the grain direction of the material is known, the values of F ty.
The maximum allowable value of kv for a rec- tangle is 1. Pressure between a lug and bushing assembly having negative clearance can be determined from consideration of the radial displacements.
After assembly, the increase in inner radius of the ring lug plus the decrease in outer radius of the bushing equals the difference between the radii of the bush- ing and ring before assembly:. Radial displacement at the inner surface of a ring.
Radial displacement »t the outer surface of a bus ung subjected to external pressure p i«. Maximum radial and tangential. The maximum radial stre.. The maximum tangential stre.. The maximum allowable press fit stress in magnesium alloys should not exceed psi. For all aluminum alloys the maximum press fit stress should not exceed 0.
Static fatigue is the brittle fracture of metals under sustained loading, and in steel may result from several different phenomena, the most familiar of which is hydrogen embrittlement.
Ultimate strength cannot be exceeded, but is not usually critical in a press fit application. The hoop tension stresses resulting from the press fit of a bushing in a lug will reduce the stress range for oscillating loads, thereby improving fatigue life.
Therefore, Hardcoat or HAE coatings should not be used in holes that will subsequently contain a press fit bushing or bearing. Figures and permit determining the tangential stress, F T , for bushings pressed into aluminum rings. Figure presents data for general steel bushings, and Figure presents data for the NAS 75 class bushings.
Figure gives limits for maximum interference fits for steel bushings in magnesium alloy rings. A method for determining the fatigue strength of T3 and T6 aluminum alloy lugs under axial loading is presented. Figures and show the lug and the range of lug geometries covered by the fatigue strength prediction method.
Fatigue lives for lugs having dimensional ratios falling outside the region shown should be corrobo- rated by tests. Ml fcZnter Figure to check that the lug dimensional ratioa fall within the region covered by the method. Enter Figure and read kj, k 2 , and kj; calculate the product kjk 2 k3. Thia extends the kik2k3 curve to cover the entire life range to static failure.
These are the conatant life lines for the particular lug being analyzed. The Goodman diagram is now complete and may be used to determine a life for any given applied stresses, or to determine allowable atresses knowing the life and P value. Given a concentric T6 aluminum lug a. If the lul Subjected to a cycle axial load. For the given lug, F. N « 1 cycle This is illustrated, for clarity, on Figure These numbers are a.
Refer to Figure The Goodman diagram is bow complete. If the known quantities are life and R value, e. Only if the lug dimensions are changed, must a new Goodman diagram be drawn. This method may also be applied to holes in sheet and other structural parts. I mar daanaaar of buying, in. Omr daa n a u a of buying, in. Innardiarnatarof lug, in.
Outar diamatar of lug, m. Z Mofcom. Product Erajwaarlng, Juna X Cosona. Product Enomaariraj,. Oapartmant of Dafanaa. Knuckla joints ara uaad in aaroapaea eonvol rods. Thay can bo raadllv dtaeonnac - rapain. Sharply necfcad rod ende differ from kip previously rlisru— d. Rafaranea 3. All angles art in degree s. Th« procedure hai been derived theoretically.
Th« proeadura tftould ba uaad in conjunction with tha fottowing tniaracbon aquation:. Oct The center of gravity of the rivet pattern Is determined by Inspection for a simple rivet pattern. Where the pattern is to complex to determine the C. The direct rivet load for this case Is determined by dividing the load "P" by the number of rivets In the pattern. The center of gravity of the rivet pattern is determined by summing up moments about reference axes as indicated below:.
The formula presented in Case 1 and 2 assume that the rivet pattern does not deform under load and that each rivet or bolt of the pattern has the same approximate fit. Large error is probable when either or both joined members display appreciable deformation within the region of the joint, such as in joints spread over a large area. The ntT. Z, since undor the latter conditions the loading peaks are rounded off, as indicated by the dotted linr-s, due to loeel plastic def orations.
Eence boaring loads conforming with tha distribution of Fig. The maximum Eicr. The r-ar-imicu shear corresponding to the load distribution of Fig. Ths distritvlio- of ccrsizt led io cccurr. After assembly, the increase in inner radius of the ring lug plus the decrease in outer radius of the bushing equals the difference between tne radii of the bushing and ring before assembly.
Radial displacement at the inner surface of a ring subjected to internal pres-. Maximum radial stress for a bushing -subjected to external pressure occurs at the outer surface of the bushing. KaxJjwm tangential stress for a bushing subjected to external pressure occurs at the inner surface of the bushing. Tor all iTumicu. Steel parts heat treated above ksi.
Ultimate strength cannot be exceeded, bu: is not usually critical in a press fit application. The presence of hard brittle coatings in holes that contain a press fit bushing or bearing can cause premature failure by cracking of the coating or by high press fit stresses caused by build-up of coating.
When a tension load is applied normal to the outstanding leg of en angle, tension, bending, and shear stresses occur- If the outstanding leg is not rigidlv supported, the allowable load is usually limited by consider- ations of permissible deflection and permanent set- If the attachment points through which the load is transmitted to the angle are not spaced sufficiently close, the full strength of the angle is not developed since local deformation at the attachment points becomes the limiting factor.
This Stress JSsbd presents design considerations and allowable loads for aluminum alloy extruded and formed sheet metal angles subjected to flange bending loads. Generous corner fillets on extruded angles and minimum bend radii on formed sheet metal angles shall be used in all cases where applied loads tend to "open" or "close" the angle.
High local stresses and large deflections in angle Joints pro- hibit their uce in applications subject to repeated or alternat- ing loads. Three 3. When tvo 2 angles are used back to back and loaded symmetric ally in both outstanding flanges, the allowables obtained from Figures 1 and 2 may be multiplied by two and one-half 2.
When tees axe loaded symmetrically in "both outstanding flanges, the allowables obtained from Figure 2 may be multiplied by three 3. The following formula will yield conservative values of deflection at the connectors:. This memo contains methods of analysis applicable to certain common types of tension fittings.
If in any application both a fitting and a casting factor are applicable, they shall not be multiplied, but only tho lexgor shall be used. This requiromont may bo relaxed upon the approval of tho Projoct Structures Engineer. Bolts highly loaded in tension should be assonblod with a washer under both the head and nut,.
Eooentrioities in fitting attachment should be kopt to a minimum. Unavoid- able eocontrioities shall be considered in the analysis. Fitting attachment edge distances ahull conform to design handbook require- ments to prevont premature tension failures in tho fitting wall. The methods of analysis of tension fittings in this r. Obtain the basio tension efficiency, , of the -wall frcm Stress Uamo Ho.
Banding Cont'd. Tension in the wall may be analyzed by the method aa shown in amo- tion I -A with tha ezoaption that A g is defined as,. A-l and Ad aboTe. See pq. End Pad Analysis Cont'd! The effectiTe Talues or a and d for the equi Talent bathtub fitting used in the analysis are giren by.
Detersdne th. Obtain the basie tension efficiency, 7? Analyte the end bolts for the oombinad loading moment plu» toneion end the oenter bolt for direct tension. To determine the bonding moment eurre, assume the oenter bolt lead computed in 2 is uniformly dietributod e-ror the bolt hoed flat.
If load-deflection test data is not available for the exact fa. Some test data is available to develop generalized stiffness curvu. Figure h. Modify the K. Aluminum Fastener, K X. Correct K:. Determine SR from Table 6. Calculate spring race for each sheet "by. Assuming that the aluminum is T6 and the titanium is 6 AV, the respective bearing yield stress allowables from Reference 1 are 78, psi and , psi.
The yield loads are then calculated to be. The flexibility is calculated for a deformation of 2 percent of the hole diameter per Section 1.
Section Education Lecture Series, 14 March The Titanium fastener values were interpolated based on Young's Modulii. Hie equation was rearranged with sane jesses, to give. When the fitting faocs. When the fitting f aoea are not in contact, shear leads.
Preload in bolt due to tightening, lba. Applied external tenaion lead, lba. See Fig. The relationship bett? Thle will ooour when the ratio of bolt preload? The averag e wrcnoh torque appliod to the nut to produoe a specified preload or strena on the roct aroa ie given by. The additive affect of the Initial preload to the applied load! Special attention should therefore be given to steel bolts through aluminum or magnoaiua fittings.
A typioal structure with a gr. Where washers are used under the nut, the fitting material shall be taken as the material of the washer.
This nemo contains an e:r. It ia applicable to all catale coicmonly used in aircraft structures. Chain epaoing ahould be used in preference to staggered spacing when- ever possible. This practice eliminates the possibility of overlooking the weakest section and reduces the possibility of premature failure. In addition, a. In suoh cases, the rivets should be in straight lines parallel to the length of the member.
If a combination of ambers giTCS different efficiencies e. When the stress varies acro. This method provides for stress conoentrstion effects at ultimate lead, insofar as the connector holes are concerned, and no additional factor Is necessary to provide for that phenomenon.
The margin of safety under an applied shear lead lead parallel the Joint ronterlino is given by. The margin of safety of the plate at the Joint in eoabinnd tension end shear is given by. Practically all periodic waves, however complicated the form, nay be considered aa being composed of, or representing the sum of, two or more sine waves.
Most waves nay be analyzed into simple harmonic or sine wave components and these components generally form a harmonic series; i. The lowest frequency is called the fundamental, and the higher ones are called harmonics. The frequency of a vibrating body is the number of complete cycles of motion In a unit time. The period of a wave is the time elapsed while the motion repeals itself. It is simply the reciprocal of its frequency. The amplitude of a wave is the maximum distance the vibrating particles of the medium in the path of the wave are displaced from their position of equilibrium.
The wavelength of a wave is the shortest distance between two particles along the wave which differ in phase by one cycle. Examples of systems possessing one, two, and many degrees of freedom are shown in Fig.
It consists of a mass "m" supported on motionless and massless rollers attached to a spring and a dashpot. If, after an initial disturbance of the system shown in Fig. This particular value of C is designated C cr where. The amplitude decreases by a definite percentage with each cycle, and the natural logarithm of the ratio of two successive amplitudes is called the logarithmic decrement. The second term gives the amplitude of the forced vibration in terms of the system constants and driving force and is called the steady state term.
The effects of rotary inertia and shear deflection are neglected. The characteristic numbers for the first three modes of this beam are: 4. The fundamental mode has a node in the middle. Higher modes are related by series of 1, 2, 3, etc. For the fixed-end column U Q is given by for a uniform. It la possible to design sonic fatigue resistant structure. Therefore, any beef -up for this type of stress must increase the stiffness without significantly increasing the mass.
Attachment of rib. Bead, are frequently used over fairly large expanse, of unsupported TesfbL.. This -Ill cause crack, to for. Again, th. This type of construction is fatigue resistant because of the large amount of structural damping.
In a clip or member being Joined whenever possible. All atiffeners ahould be dealgned using the rule of thumb that eymmetrioal attachments will prolong aervica Ufa. Thicker gagaa will probably b« neceaaary for each apecial eaae. One of the moat critical regions of a etiffened panel la the change In stlffnesa st the end of a atiffaner.
This tranaition must be as gradual as poealble with relatively low etreaaea in the fastener. The atreaaea in curved panels are much lower than in flat plates, if the plate width is more than a email percentage of the radius of curvature. This results from the pressure loads being carried as membrane stresses like hoop tension instead of by bending.
Anything that might possibly produce a stress raiser should be avoided. A majority of the falluree due to sonic excitation can be attributed to stress concentrations at rivet holes, small bend radii, raw edgea, reentrant comers, rough machine surfaces, etc. Goldbrlck, R. Panel flutter is a self-excited, aeroelastic instability that may occur when a panel is exposed to a supersonic airstream.
During flutter the panel oscillates in a direction normal to its plane and the amplitude of motion usually increases until limited by inplane stresses. The consequences of panel flutter cannot be reliably predicted, but the serious effects that have been encountered include very high noise levels vithin occupied compartments as well as panel failure due to fatigue.
A considerable amount of work, both experimental and theoretical, has been done during the last two decades not only to obtain insight into the phenomenon but to develop procedures for the prediction and prevention of panel flutter. This report presents the results of an extensive investiga- tion to determine the state of the art in panel flutter, and from that basis, to formulate a comprehensive set of design criteria. The investigation con- sisted not only of literature review but also of personal consultation with individuals who have made significant contributions in the field.
The report further brings together data from wind tunnel test, flight test, vibration test and theoretical investigation f and presents methods that have been developed to provide procedures, criteria, and guidelines for designing panels.
General ruidelines eased on comparative tciL. To understand the problems created by sonic fatigue, it is necsaaiiry to be familiar with so. A sound is esscniuJIv a fluctuating pressure in air or some other medium. The intensity of a sound is determined by the amplitude of the pressure waves and is commonly expressed in Jcc.
Expressed malhematirrUy. The pressure awodated with a fc-ven Jccibel level is shown in Fig. With the jet engines presently m u«e f ' 70 JBj. J thereby obtain a picture of the correspondence of frequencies and noise leveis. The responie of a panel to random noise is somewhat unpredictable, but a typical response mitfhi be a resonant frequency vibration.
The amplitude of this. A ample oscillator may bt characterized by its resonant frequency j, of ha rcJatrft damping 4" and the elastic r e sponse y 0 to tome reference forcing input Fg.
The testing has taken three defmiic fonm: testing of high-speed components for buffeting and nutter, behind and within a jet blast; testing of simulated panels behind -a jet engine in a test cell; and testinf of simulated panels in a sound chamber with a controlled sound source.
The lectins; program, coupled with extensive service life experiences, has provided some design guidelines. Generally, the test results provide retime life data for variations in design detaiis in riveted sheet structure up through fully bonded sandwich construction in mc: Jg as well as some plastics. Some of the early comparative lest results arc utovr.
The service experience and test programs from the B, KC, and commercial fleets have provided information that can be accepted is appropriate stude- Mnes for structure in sonic arras. The tonic designs are not enact: however, their use should prevent pro it errors.
The design curves shown' in Fig. The service experience of present jei xirciaft has shown that a panel, designed for The curves are plotted for souare panels: the correction fact on for rectangular panels arc given in Fig. The object of experimental at re a a analysis Is to determine the stress distribution in a structure from strain measurement. If the directions of the principal stresses are known, only two strain measurements are required.
It can be shown by Hoolce's law that if the directions are known, the stresses can be obtained by making use of the following formulas t. If the direction of the principal stresses are unknown, the problem is sonewhat more complicated. Consider the axes shown in Fig. In Fig. The strains along axes A , B , and C will have the following relationships with the x and y axes of Fig.
By using the equation for maximum shear and Hooke ' s law, the principal stresses can be obtained from the following formulas. The use of Mohr ' b circle la very helpful in the reduction of strain gage data. Mohr's circle la conatructed ao that the vertical axis represents a hear atraln and the horizontal axis represents the axial strains.
The axial strains measured by the U5 0 rosette are plotted on the horizontal axis. The radius, R , can be obtained as follows:. Pind the principal strains and principal axes of strain and compute the principal stresses if.
Compute the. MOTE: A positive atrain aignifles tension. Positive and negative strains are to be added algebraically. Kelly, F. Press, The conventional team theory tased on the assumption that a plane section before tending remains plane after tending gives a linear distribution of strain and stress in the elastic range i.
In the plastic ranee, hovever, although the strain distribution is assumed to remain linear, the stress distribution corresponds with the stress-strain relationship for the material. An approximation of this distribution has been obtained, which enables the prediction of the effects of the shape and material properties on tending in the plastic range. This Stress Memo shall not be used for round tubes. Bound tubes shall be analysed in accordarce with Section Q m is the static first moment, about the principal axis, of the area between the principal axis and the extreme fiber.
I is the moment of inertia of the whole section about the principal axis and c is the distance from the principal axis to the extreme fiber. Note: When section being checked contains holes, Q m and I are to be calculated using the net section. Repeat 1 uiinz the allowable yield stress Fty to obtain the allowable yield moment!!
This method of determining bending allowables has been substantiated by tests on aluminum alloy castings And forgings, and on magnesium forglngs of relatively thicic-walled sections only. Use following method when resultant applied moment vector is parallel to a principal axis which is not an axis of symmetry. In utilizing Figure 1, the k value for each part cocputed as above will be the same as for a symmetrical section composed of the giver, part and its reflection about the principal axis of the original section-.
Note: When section being checked contains holes, Q m and I are to be calculated usir. Enter the graph with this strain e s and obtain the corresponding stress from the stress-strain curve. Obtain ultimate and yield margins of safety as explained pg. This car.
Select several values of strain for extreme fiber of part having larger c, and for each value of strain compute corres- ponding moment, as explained above. Plot total moment against strain; the strain corresponding to the given applied moment is then the actual strain at the extreme fiber, and the stress at any point in the section can be founc therefrom by obtaining the proportionate strain at the point in question and reading the corresponding stress from the stress- strain curve.
The formulas are applicable when bending is about a principal axis and the shear load Is perpendicular to this axis. By the method of Section H-C, determine the strain produced in the extrer. Use the extrfime fiber on the same side of the principal axis as the section for which the shear flov is being deter- mined.
When the shear flov Is being determined at the priiiclpal axis, compute values Uit"-5 both parts of the section and use the larger. Enter the stress-strain curve vith this crippling stress and determine the strain of the critical portion e y.
Enter the graph plastic "bending with the strain determined in C and determine the corresponding stress from the stress-strain curve. I and c defined in Section II-A and add the two resulting moments to obtain the allowable moment, M, which will subject the critical fiber to its crippling stress. This coalition occurs vhen the resultant applied moment vector is nox.
Let X and Y represent two mutually perpendicular centroidal axes. Let X' and Y' represent the principal axes. Moment vectors are designated by double headed arrovs and are to be interpreted by the left hand rule i. Any case of complex bending nay be resolved into two cases of simple bending about the principal axes of the section.
Sections I anl U. Sections I an! Resolve the applied shear force into components parallel to the principal axes". The maximum shear stress in a beam usually occurs at the principal axis, vhere the bending stress is zero.
The maximum bending stress occurs at an extreme fiber, vhere usually the shear stress is zero. In - the elastic range , the distribution of shear and bending stress is usually such that the most critical point in the section is at either the principal axis or the extreme fiber.
This is true on a rectangular section since the shear distri- bution across the section is parabolic and the bending distribution is linear. If the shear dis- tribution had been elliptical every point in the cross section vould be equally critical In ccm- binded stress based on circular interaction.
In the plastic range however, the distribution of the shear stress as veil as the bending stress differs from that in the elastic range. This results in intermediate points vhich frequently become more critical in combined stress than either the shear stress at the principal axis or the bending stress at the extreme fiber. Parabolic shear. To find the most critical point vould require calculation of cccbined stresses at a series of points across the section. The maximum shear stress does not alvays occur at the principal axis.
Note: " The margin thus obtained is not a "true" margin of safety, since its Yariation with applied load is non-linear; but if the calculated margin is positive the true margin is positive, and if the calculated »arSn is negative the true margin is negative. The margin of safety as computed above shall be used for formal stress analysis. If the "true" margin of safety is desired, it may "be obtained "by a trial and error procedure in which the loading is varied all loads varied in sane proportion until the loading is found for which the margin of safety as determined ebove is zero.
This loading becomes the allowable, and the true margin of safety is given by:. Such points must be. Ordinarily points such as B in the sketch, even though highly stressed in both shear and bending, are protected by possible redistri- bution, hence are adequately covered by the interaction of Section C above, and should not be checked locally. To check a point for local interaction, obtcin true shear stress accord- ing to Section HI ani true bending stress according to Sections I-S and.
For complex bending, R. Plot R. Draw OA and extend to its inter- section B with the appropriate curve according to the value of n obtained in Section E. When shear acts in addition to bending and tension, the calculation of shear flow as explained in Sections III and VI and the interaction of shear and bending Ref. Section VII must be modified. Denoting this stress by f total , obtain:. Obtain a - OA, b. The Taxlnun shear stress does not always occur at the principal axis.
For complex bending, obtain maximum shear stresses in berth direct ion, f f and f , based on the shear flews:. Plot R c , on Figure k as point A. Drav OA and extend to it3 inter- section B vith the curve n « 1. The yield margin of safety of a "beam under cabined leading shall be obtained by means of S. To investigate yielding of a compact structure crippling or buckling not pertinent , under the action of two dimensional combined stress, interaction curves should not be used.
Instead, a maximum "equivalent" stress ratio R is computed and a margin of safety obtained therefrom:. I is given by the following formula which is based upon the "maximum dis- tortion strain energy" criterion for yielding :. Stress ratios due to direct or bending stress are positive for tension and negative for compression; care must be taken that signs are correct. Sub- scripts 1 and 2 indicate directions which are mutually perpendicular. If it is. E 3 is a shear stress ratio due to coabinins sinple shear aid torsional shaar and is given byi.
S60 kit L. Mufilnum Alloy "xtmalon.!? Obtain R f roa curves only for at»at« banting vlth no axial load. Othervlaa HI tart. Obtain P. Otherwiaa ace text. These curves provide yield and ultimate modulus of rupture values for symmetrical sections only.
For materials with significantly different tension and compression stress-strain curves, the necessary corrections for shifting of the neutral axis are already included. In the case of work hardened stainless steels in longitudinal bending with all fibers in tension as in pressurized cylinders , the transverse Modulus of Rupture Curves are applicable.
It is recommended that Referenced or other official sources be used for allowable material properties. Where material allowables vary with thickness, cross-sectional area, etc. Heat Treated. Heal Treated. Thickness s 0. Thlckneii 0. Thickness 0. Thickness aO. TOcknaia x. Thlckneaa s 0. Minimum Bending Modulu. F H - lift. Thickness s. Ml la. SO la. OJI ta. SI 1b. Longitudinal Thtckneii 5 1. Plastic bending curves found in Section Deflections of statically determinate structures due to bending with any or all fiber stresses in the plastic range can be readily determined.
Partially or completely plastic statically indeterminate structures can also be solved by procedures similar to those used in the Elastic Energy Theory. Other elastic theories could have been extended as well to include plastic bending effects but the Elastic Energy Theory was chosen due to its simplicity and common usage. Elastic theories are accurate only if no part of a structure Is stressed beyond the proportional limit of a material no plastic strain.
In structures designed to stress levels beyond the proportional limit, the error of an elastic deflection analysis is dependent on the amount of plastic strain involved. Therefore when deflection is a limiting factor and plastic strains are involved, an analysis such as the Elastic- Plastic Energy Theory should be used.
If the deflections are then the most critical design condition, the margin of safety becomes. Equation Energy is conserved; i. Plane sections remain plane; i. The deformations are of a magnitude so small as to not materially affect the geometric relations of various parts of a structure to one another. A - real vertical deflection of a beam at the point of application of a virtual load. For beams with varying cross-section, c may be a variable. A rectangular beam, simply supported at the ends, is subjected to a con- centrated vertical load at its center.
Find the vertical deflection of the beam at its center. Load: P » lb. Apply a virtual 'unit load, Q, at the beam center and construct the virtual moment diagram, m. Enter the plastic bending curves in SZC. Partially plastic fiber stresses existed only over the middle 8 inches in this example. The elastic. Many parte In various coupononts of the airplane ero subjected to frequent applications of near-limit loads during the servico life of the airplane.
The linkage, attachnent lugs and other carry-through parts of the landing gear retracting mechanism, hinges and latches of cabin door and emergency exits are typical examples of parts falling into euon a category.
It is readily apparent from the examination of any typioal S-H curve that the number of load applications that can be euctainod when high loads are applied are relatively low. Thus to insure adequate servioe life it be- comes necessary to provide limitations on tho degree of exploitation of the -. Another category of parts requiring special consideration from a fatigue standpoint are those designod by the use of bending noduluo of rupture.
This oan be verified by examining any of tho curves in secru fl. O For example In Figure 14 for stoel at a ksi level. It is therefore obvious that some limitation on the exploitation of modulus of rupture is necessary when the spread between operating loads and design limit loads is not large. In order to provide adequate strength and insure trouble-free servioe during the useful life of the airplane, this memo establishes policies for the detail design and analysis of parte falling in the categories discuosed above,.
This memo Is not applieable to the shell components of the airplane since fatigue problomo" in sueh structure S3aT"be given more detsiled oons idoration. Therefore, extreme care and judgement are to be exerolaed in a electing components to which thia memo is to be applied.
All o opponent a ao oho a en are to be ealled to the attention of the Projoot Structures Engineer for approval with regard to use of thia memo. Parte and syatems falling into this category may roquire a formal fatigue analysis.
However, if a formal fatigue analysis ia not made, the following requirements shall be ad- hered to. For steel with mlnlflsns speoified heat treat varying between and ksi, linear interpolation of the reduction factor may be used. Por the. Home Design 6 v6. Internet Accelerator 3 v3. Media Sync v1. Movie Studio Pro 3 v3. Music Studio v1. Music Studio 8 v8. Office 8 v Office Free v PDF Free v2. PDF Pro 2 v2. PDF Pro 3 v3. Photo Commander 16 v Photo Converter 2 v2.
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