Materials And Structural Systems

Step 1: Understanding the frame.
The given frame is a portal frame with two fixed columns and a rigid beam at the top. A horizontal load of 80 kN is applied at the top of the left column. Both columns have the same height (3 m), and the beam length is also 3 m. All members have the same moment of inertia.

Step 2: Distribution of horizontal load.
Since the frame is rigid and symmetrical in stiffness, the horizontal load will be shared equally by the two columns. Hence, each column will resist half of the horizontal shear:

Step 3: Moment in the left column.
The maximum moment at the fixed base of the left column is given by: where (shear in left column) and .

Step 4: Analysis of options.
- (A) 120 kN.m: Correct, matches our calculation.
- (B) 240 kN.m: Would be true if the entire 80 kN load acted only on the left column, but due to frame action, it distributes.
- (C) 160 kN.m: Incorrect, does not match equilibrium conditions.
- (D) Zero: Not possible as the load generates moment.

Step 5: Conclusion.
The maximum moment in the left column is .

Step 1: Analyze A.
"Plane section remains plane before and after bending" is the fundamental assumption of bending theory (Bernoulli's assumption). It gives linear strain distribution. So, A → II.

Step 2: Analyze B.
"Material is elastic and deflections are small" implies elastic analysis where superposition holds good. Hence, B → I.

Step 3: Analyze C.
"Uniqueness theorem" ensures a unique solution in structural analysis, applied in non-linear stability/buckling problems. Thus, C → III.

Step 4: Analyze D.
"Large deformation" concept is used in plastic analysis to determine the collapse load. So, D → IV.

Step 5: Conclusion.
The correct matching is:

Step 1: Analyze each structure.
- (A) Truss → Members mainly carry axial force → Structural behavior: Shortening (III).
- (B) Beam → Designed to resist bending → Structural behavior: Bending (I).
- (C) Column → Prone to buckling → Structural behavior: Buckling (IV).
- (D) Shaft → Transmits torque → Structural behavior: Twisting (II).

Step 2: Matching.

Step 3: Conclusion.
The correct match corresponds to option (4).