Subject : Structural Analysis 1

Topic :Hinge Arches

Difficulty : Medium

1) Support reaction ($rx^n$) calculation:

Step 1 Consider part (CA)

$BM_c = 0$

$V_A \times 6 - 30 \times 6 \times \frac{6}{2} - H \times 4 = 0$

$6V_A - 4H - 540 = 0$

$V_A = \frac{4H + 540}{6}$ -------- (1)

step 2 part (CB)

$BM_c = 0$

$V_B \times 10 - H \times 8 - 120 \times 3 - 220 \times 7 - 30 \times 10 \times \frac{10}{2} = 0$

$10V_B - 8H -360 - 1540 -1500 = 0$

$10V_B = 8H + 360 + 1540 + 1500$

$10V_B = 8H + 3400$

$V_B = \frac{8H + 3400}{10}$ ---------- (2)

Step 3

$\sum F_y = 0(\uparrow +ve)$

$V_A + V_B - 30 \times 16 - 120 - 220 = 0$

$V_A + V_B = 820$ --------- (3)

$\frac{4H+540}{6} + \frac{8H+3400}{10} = 820$

$\boxed{H = 265.90 KN}$

Put in equation (1)

$V_A = \frac{4H + 540}{6}$

$V_A = \frac{4 \times 265.90 + 540}{6}$

$\boxed{V_A = 267.27 KN}$

Put in equation (2) H = 265.90 KN

$V_B = \frac{8H + 3400}{10}$

$V_B = \frac{8 \times 265.90 + 3400}{10}$

$\boxed{V_B = 552.72 KN}$