Aluminum Co. of America said yesterday that its second-quarter profits rose 31 percent over last year, despite a month-long strike by 15,000 union members.

Also yesterday, RJR Nabisco Inc. said its net rose 21 percent in the quarter; Bell & Howell Co. said it suffered a 21 percent dip in second-quarter earnings, and Sperry Corp., in its final earnings report, said its profits fell 87 percent in its first fiscal quarter, mainly because of special costs related to its acquisition by fellow computer maker Burroughs Corp.

Alcoa, which is based in Pittsburgh, said net income for the three months was $53.3 million (63 cents a share). In the same quarter last year, Alcoa earned $40.6 million (49 cents) after a $15.6 million charge from a utility rate case at a subsidiary.

For the first half, Alcoa reported earnings of $54.7 million (64 cents) compared with $47.3 million (57 cents) in 1985. Sales and operating revenue for the periods declined to $2.41 billion from $2.68 billion.

Alcoa Chairman Charles Parry said second-quarter earnings improved because of a more profitable product mix, price and cost improvements and a favorable foreign currency exchange.

Shipments of aluminum products by the nation's largest aluminum producer were 384,000 tons in the second quarter, a 17 percent drop from 462,000 tons in 1985. Sales and operating revenue also declined to $1.23 billion from $1.36 billion, the company said.RJR Nabisco Inc., a Winston-Salem, N.C., consumer products company, said Thursday that its earnings were $276 million compared with $228 million during the same period last year. Earnings per share were 99 cents, up from 86 cents. Consolidated net sales were $5.3 billion, up 55 percent from $3.4 billion last year.

Record sales and operations in the quarter reflected gains in the company's two key lines of business -- tobacco and foods and beverages.

Six-month earnings were $482 million ($1.65), up 18 percent from $410 million ($1.52) in the first six months of 1985. Net sales were $9.9 billion, up 57.2 percent from $6.3 billion. Bell & Howell Co. said its second-quarter earnings decline came despite a 12 percent increase in revenue to $210 million.

Poor results in textbook publishing and videocassette duplication were cited as the primary causes of the profit drop.

Earnings per share were 65 cents compared with 84 cents a year ago, the company said.

Profits for the first six months were $11.3 million ($1.06), down 16 percent, on sales of $398 million, up 12 percent. Sperry Corp. said it earned $6.8 million (12 cents a share) in the April-June quarter, down from $51.5 million (91 cents) a year earlier. Sperry said its second-quarter earnings would have been $44.4 million (75 cents) except for the costs of its merger into Burroughs Corp.

J. Peter Hynes, a Sperry spokesman, said the biggest costs were fees paid to bankers and lawyers while Sperry was fighting the Burroughs takeover bid and the cost of canceling employe stock-option programs. Employes were paid as if they had exercised all their options to buy Sperry stock, he said.

Revenue for the quarter rose 1.8 percent to $1.26 billion from $1.23 billion a year earlier.

Burroughs, based in Detroit, acquired control of Sperry on June 11.