Question

A rigid jointed frame ABCDE is formed such that all the members are joined rigidly at 'B' as shown below. If the span BC is subjected to UDL of intensity 12 kN/m and the span BD is subjected to a central concentrated load of 40 kN, then moment developed at end D & E respectively are:

• A. $3.33,4.43$
• B. $20.93,4.43$
• C. $8.86,-3.14$
• D. $18.65,-9.05$

Answer 1

The correct option is B $20.93,4.43$


$k_{BA}=\frac{3EI}{4};D{F}_{BA}=0.117$

$k_{BC}=\frac{3EI}{3};D{F}_{BC}=0.156$

$k_{BD}=\frac{8EI}{3};D{F}_{BD}=0.416$

$k_{BE}=\frac{8EI}{4};D{F}_{BE}=0.311$

Joint	$A$	$D$	$B$	$E$	$C$
Member	$AB$	$DB$	$BA$	$BD$	$BE$	$BC$	$EB$	$CB$
$DF$	$1$	$0$	$0.117$	$0.416$	$0.311$	$0.156$	$0$	$1$
FEM Bal	$0$	$15$	$0$ $3.33$	$-15$ $11.86$	$0$ $8.86$	$-13.5$ $4.45$	$0$	$0$
C.O		$5.93$					$4.43$
$\sum M$		$20.93$	$3.33$	$-3.14$	$8.86$	$-9.05$	$4.43$

$\therefore M_D=20.93kN-m\&M_E=4.43kN-m$