For the given SFD, First we draw the load diagram, and then with the help of load diagram we draw the BMD.
As the slope in SFD is zero. So it indicates that the beam is only subjected to point loads. Let RA and RB be the support reaction at A and B and the load RC, RD and RE in down ward direction at point C, D and E respectively.
Here the graph of SFD moves from A-F-G-C-D-H-E-J-K-B
Consider two points continuously,
Consider A-F
Load moves from A to F
Load intensity at A = RA = Last load - first load = 3.5 - 0 = 3.5KN
i.e. RA = 3.5 KN ...(1)
Consider F-G
Load moves from F to G
Load intensity = Last load - first load = 3.5 - 3.5 = 0
i.e. No load between F to G ...(2)
Consider G-C Load moves from G to C,
Load intensity at C = RC = Last load - first load = 3.5 – 1.5 = –2KN
i.e. RC = –2 KN ...(3)
Consider C-D Load moves from C to D,
Load intensity = Last load – first load = 1.5 – 1.5 = 0 i.e.
No load between C to D ...(4)
Consider D-H Load moves from D to H,
Load intensity at D = RD = Last load - first load
= -1.5 – 1.5 = –3KN i.e. RD = –3 KN ...(5)
Load moves from H to E,
Load intensity = Last load - first load = -1.5 -(-1.5) = 0 i.e.
No load between H to G ...(6)
Consider E-J Load moves from E to J,
Load intensity at E = RE = Last load - first load
= –1.5 -(–3.5) = –2KN i.e. RE = –2 KN ...(7)
Load moves from J to K
Load intensity = Last load - first load = –3.5 – (–3.5) = 0
i.e. No load between J to K ...(8)
Consider K-B Load moves from K to B,
Load intensity at B = RB = Last load - first load = 0 –(–3.5) = 3.5KN
i.e. RB = 3.5 KN ...(9)
Now load diagram is given in fig 12.30
Now Calculation for BMD
Taking moment about any point gives the value of BM at that point
Consider left portion of the beam
Taking moment about point A i.e. MA = BMA = 0
Taking moment about point C, MC = BMC = 3.5 X 2 = 7KN-m
Taking moment about point D, MD = BMD = 3.5 X 4 – 2 X 2 = 10 KN-m
Taking moment about point E, ME = BME = 3.5 X 6 – 2 X 4 -3 X 2
= 7 KN-m
Taking moment about point B, MB = BMB = 3.5 X 8 – 2 X 6 – 3 X 4 – 2 X 2= 0 KN-m
Draw the BMD with the help of above value.
