Step-by-step explanation:
To calculate the maximum shear stress (Tmax) and the shear stress at point A (TA) in the given beam, we can use the formula for shear stress:
Shear Stress (τ) = V / A
where V is the shear force and A is the cross-sectional area subjected to the shear force.
Given data:
Shear force (V) = 12 kN = 12,000 N
Dimensions of the cross-section:
Width of the web (20 mm)
Height of the web (200 mm)
Height of the flange (20 mm)
Length of the flange (300 mm)
Step 1: Calculate the cross-sectional area of the web (A_web):
A_web = Width * Height
A_web = 20 mm * 200 mm
A_web = 4000 mm²
Step 2: Calculate the cross-sectional area of one flange (A_flange):
A_flange = Width * Length
A_flange = 20 mm * 300 mm
A_flange = 6000 mm²
Step 3: Calculate the total cross-sectional area subjected to the shear force (A_total):
A_total = A_web + 2 * A_flange (since there are two flanges)
A_total = 4000 mm² + 2 * 6000 mm²
A_total = 16000 mm²
Step 4: Calculate the maximum shear stress (Tmax):
Tmax = V / A_total
Tmax = 12,000 N / 16000 mm²
Tmax = 0.75 N/mm²
Step 5: Calculate the shear stress at point A (TA) at the top of the beam's web:
TA = V / A_web
TA = 12,000 N / 4000 mm²
TA = 3 N/mm²
So, the maximum shear stress in the beam (Tmax) is 0.75 N/mm², and the shear stress at point A (TA) at the top of the beam's web is 3 N/mm².