Question

A loaded beam with a pin support at B and a roller support at C is shown in Figure 1. The applied loads on the beam are: an anti-clockwise point moment at A, a variably distributed load between B and C, and a clockwise point moment at D.

A loaded beam with a pin support at B and a roller support at C is shown in Figure 1. The applied loads on the beam are: an anti-clockwise point moment at A, a variably distributed load between B and C, and a clockwise point moment at D g kN/m fANm h kN*m B C 2 m 2m 4 m Figure 1 The magnitude of the anti-clockwise point moment f in units of kN*m can be found by summing the 1st, 2nd and 3rd digits of your student number. The magnitude of the variably distributed load g in units of kN/m over support B is equal to the sum of the 1st, 2nd, 4th and 5th digits of your student number. The magnitude of the variably distributed load over The magnitude of the clockwise point moment h in units of kN*m is equal to the sum of the 1st, 2nd, 6th and 7th digits of your student number. support C is 0 kN/m 1767437 For example, if your student number is: 14 kNm Magnitude of the anti-clockwise point moment f is equal to 1+7+6 Magnitude of variably distributed load g is equal to 1+7+7+4=.19KNM Magnitude of the clockwise point moment h is equal to 1+7+3+7=18KNM = 5) Determine the bending moment equations for all segments of the beam if the datum used is Point D. Please express all equations in decimal format (no fractions). Marks will be deducted for equations that use Point A as the datum. 6) Hand draw the bending moment diagram and annotate the values at positions A, B, C and D 7) Identify the magnitude of the bending moment and the location on the beam between the supports at B and C where the bending moment has a local maximum. The location should be relative to the datum at Point D.

Answer 1

fo (G) I 4 KNm 19 KN.m (2) 2m 2m h 18 KNm By

6+ve) 2 =B O B.yt Cy-xx) + (b1 Xt) But Cy 38 38 Mo-O (2 +ve) C (33x )+ 18- 14 こ0 Cy 152 = 13-67 KN t 41 Cy 3 B 6Vom ( 24 33 K N Byこ38-13.67

PoYtion C- D h Ox2nm +ve) EM O 18 KN Tm C-D B C Portion &-2 (-2) (-2) 2h D -2 2 2 Cy D 97X72 19 Cu M X-2 19 (-2) dix

(メー2)(メ-2) M-h+ Cy (x-2) - 2,375 (メー2) + 18-13-67(x- 2) 792 (-2) 18 13. 61 (-2) 13-C メー467133」 38 PoYtion A-Bi- 87メ>9 M 0 G+ve) M-h+Cy (x-)+y (x6) 2m - 38 (-4.67 24.33 (x-6)-13.67(-2) +18 ヲ M= 38(X-4,6) A-B

09Yo: 18 KN.m 81 29 2m +ve +ve A ve 2m uuth -14 14 T The moment (bending Maximum at c' moment) tYom Point D. which is 18 KN.m