MINISTRY OF EDUCATION AND SCIENCE OF UKRAINE. National aerospace university Kharkiv Aviation Institute. Department of aircraft strength

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1 MINISTRY OF EDUCTION ND SCIENCE OF UKRINE Nationa aerospace uniersity Karki iation Institute Department of aircraft strengt Course Mecanics of materias and structures HOME PROBLEM 6 Graps of Sear and Norma Forces and Bending Moment Distribution in Pane Bending of Staticay Determinate Frames Name of student: Group: disor: Data of submission: Mark:

2 > < In norma force cacuating, we wi use te rue tat norma force in te cross-section is numericay equa to agebraic sum of eterna forces appied to te rigt or to te eft part of te rod after its irtua cutting according to te metod of sections. Tensie eterna force soud be substituted into te equation wit positie sign and isa ersa. Tis sign conention is sown on Fig. 1. Sear force in an arbitrary section is equa to te agebraic sum of a eterna forces projections on te -ais of cross-section, but ying ony on one side of te section (eft or rigt) (see Fig. 1). Te bending moment in a section is equa to te sum of moments, in reeance to te transerse ais in te section, of a eterna forces appied to one side of te section (eft or rigt) (see Fig. 1). а) for norma force b) for sear force N > б) for bending moments > Fig. 1 N < < Q < Q > Comment: in te case wen te curature of defected beam cure is coincident wit -ais direction, corresponding component of bending moment equation wi be assumed to be positie and ice ersa. Te grap of bending moment wi be designed on tensie fibers of te beam since position of tensie fiber is cear in bot situations sown on Fig. 1.

3 Soution 1. Drawing te frame in scae and appying te support reactions in arbitrary directions. Fig.. Cacuating te reactions in supports R, R, M R. Since te reactions actua directions are unknown we wi direct te reactions arbitrary (see Fig. ). Te reaction positie sign from future cacuating wi mean tat te reaction origina direction is coincident wit actua one and ice ersa. In reactions cacuating, we wi use two momentum equations of equiibrium (reatie to and C points) and aso equation of force equiibrium in ertica direction. Note, tat in designing te momentum equations of equiibrium cockwise rotation wi be assumed to be negatie and ice ersa. (1) M = q M P P+ q MR =, q MR = q M P + = 3 8 8= 19 knm. "Minus" sign of M R moment iustrates tat its actua direction is opposite to preiminary assumed i.e. M is directed countercockwise. It is sown on Fig.. R () MD = q + RА M + q + P+ MR =, R А q + M q + + P MR = = = kn. 3

4 "Minus" sign of assumed i.e. А R А reaction iustrates tat its actua direction is opposite to preiminary R is directed to eft. Tis is sown on Fig.. (3) P = q R =, R = q = 1 =+ kn. 3. Seecting te arbitrary cross-sections at -distances from te origin of eac potion and writing te equations of norma and sear forces and aso bending moment functions. In tis soution, te portion baance wi be considered to get te most simpe equations of interna forces: te portions I-I and II-II wi be considered from D point (motion from D to B point), potion III-III wi be considered upward from E point and ast portion wi be considered from point to rigt. Tis is sown on Fig.. I I ( < < ) I I I q N ( ) = kn, Q ( ) = q = = = = kn, M ( ) = = = = = knm. II II ( < < ) II II N ( ) = q = kn, Q ( ) =+ P= 4 kn, II q y M ( ) = + P = = = = 6 knm. III III ( < < ) III III III q y N ( ) = kn, Q ( ) =+ P q = = 4 = = kn, M ( ) = P + = = = = 8+ = 6 knm., ( < < ) А ( ) =+ А = kn, y А R N ( ) =+ R = kn, Q R M ( ) = R M = = 19 = = 4 19= 15 knm. 4. Designing te graps of norma and sear forces and aso bending moment distribution. Bending moment grap wi be drawn on tensie fibers according to te sign conention mentioned aboe (see Fig. 1). Te graps are sown on Fig. 3. 4

5 N ( ),kn Q ( ),kn ( ),knm Fig. 3 5

6 5. Cecking te baance of two infinitey itte eements of te frame. Fig. 4 6

Instructional Objectives:

Instructional Objectives: Instructiona Objectives: At te end of tis esson, te students soud be abe to understand: Ways in wic eccentric oads appear in a weded joint. Genera procedure of designing a weded joint for eccentric oading.